determination of batch-sizes - produktionsekonomi
TRANSCRIPT
i
Faculty of Engineering
Department of Industrial Management and Logistics
Division of Production Management
Determination of Batch-Sizes A case-study in the process industry. Master Thesis in Production Management β MIOM01 Spring 2018
Authors
Simon Gottfridsson
Viktor FarbΓ€ck
Supervisors
Johan Marklund, LTH
Fredrik Johansson, The Company
Examiner
Peter Berling, LTH
ii
Acknowledgements
We would like to thank everyone that have in any way been a part of this thesis. Special
thanks are extended to Johan Marklund, our professor and supervisor at Lund University for
all his time and valuable inputs and to Fredrik Johansson, our supervisor at the company
who have been a constant support.
Our gratitude is also extended to all lecturers and students that have made our time at the
mechanical engineering program, and in turn the supply chain management program at LTH,
to valuable experiences.
iii
Abstract
Title Optimization of batch sizes, A case-study in the process industry. Course Degree Project in Production Management β MIOM01 Authors Simon Gottfridsson and Viktor FarbΓ€ck Supervisor Johan Marklund, LTH & Fredrik Johansson, the company. Background and Research question The company have a complex product portfolio and production facility. Currently, the batch sizes in production are based on experience and is not based on any cost analysis. The central organization have recently put more emphasis on the batch sizes, especially in a context of increasing the efficiency of the packaging lines. The company wishes to investigate the batch sizes and analyze the consequences of implementing a method to calculate batch sizes from a cost perspective. Methodology The chosen research method is a balanced approach which incorporates both qualitative- and quantitative research. Interviews and archive analysis was used to develop an understanding of the problem and obtaining data for a quantitative analysis. The research took place at the company and the data was collected from the companyβs IT systems. Theoretical Framework Theory relevant to the problem at hand was first studied and is presented in the report. This theory is well-established in operations research and is used as both a foundation to analyze the current situation as well as a base for suggestions of how to solve the companyβs problems. Conclusion The EOQ model was chosen as a suitable theoretical model for the company. During the analysis, several findings were made regarding the current approach of determining costs and managing the inventory. The current approach of determining batch sizes encourages a reactionary way of thinking for operational planners where the most important SKUs are shown most regard due to pressure from top management. The current way of calculating safety stock have also been shown to greatly discourage an increase in batch sizes, even though an increase could both be cost-effective and increase efficiency in production. Hence, a new theoretically sound method to calculate safety stock s suggested. The report presents an approach that takes cost, the perishability of products and operational constraints into account and provides the company with an Excel based decision making tool. Keywords Lotsizing, Changeover cost, Holding cost, Safety stock, EOQ, Process industry.
iv
Content Acknowledgements ................................................................................................................ ii
Abstract ................................................................................................................................. iii
1 Introduction .................................................................................................................... 1
1.1 Background ............................................................................................................. 1
1.2 Problem Description ................................................................................................ 1
1.3 Purpose ................................................................................................................... 2
1.4 Delimitations............................................................................................................ 2
2 Methodology ................................................................................................................... 3
2.1 Research purpose ................................................................................................... 3
2.2 Research Design ..................................................................................................... 3
2.2.1 Company case study ........................................................................................ 3
2.2.2 Modelling .......................................................................................................... 3
2.3 Research Techniques ............................................................................................. 4
2.4 Problem Description ................................................................................................ 4
2.4.1 Interviews ......................................................................................................... 4
2.4.2 Observations .................................................................................................... 5
2.4.3 Archive analysis ............................................................................................... 5
2.5 Research Approach ................................................................................................. 6
2.6 Research Strategy................................................................................................... 6
2.7 Quality Assurance ................................................................................................... 7
2.7.1 Reliability .......................................................................................................... 7
2.7.2 Validity ............................................................................................................. 7
2.7.3 Representativeness.......................................................................................... 7
2.8 Chosen methodology .............................................................................................. 7
2.8.1 Used Methodology ........................................................................................... 7
2.9 Working procedure .................................................................................................. 9
3 Theoretical Framework ..................................................................................................11
3.1 Strategic levels of organisations .............................................................................11
3.2 Sales and Operations Planning ..............................................................................11
3.3 Enterprise Resource Planning ................................................................................12
3.4 Lot Sizing ...............................................................................................................13
3.4.1 The Economic Order Quantity .........................................................................13
3.4.2 Wagner-Whitin ................................................................................................15
3.4.3 Silver-Meal ......................................................................................................15
3.5 Critical Variables ....................................................................................................16
v
3.5.1 Holding Cost ...................................................................................................16
3.5.2 Activity Based Costing .....................................................................................17
3.5.3 Changeover Cost ............................................................................................17
3.5.4 Shortage Cost .................................................................................................17
3.6 (R, Q) Policy ...........................................................................................................17
3.7 Service Levels and Safety Stocks ..........................................................................18
3.8 Yield loss ................................................................................................................19
3.9 Statistical Theory ....................................................................................................19
3.9.1 Linear combinations of stochastic variables ....................................................19
3.9.2 Statistical fitting ...............................................................................................20
3.9.3 π2-test .............................................................................................................20
3.9.4 Kolmogorov-Smirnov test ................................................................................21
4 Empirical Context ..........................................................................................................23
4.1 Supply chain...........................................................................................................23
4.2 Processing .............................................................................................................24
4.3 Packaging ..............................................................................................................24
4.3.1 Production Fulfilment .......................................................................................25
4.3.2 Changeover Process .......................................................................................25
4.3.3 Line Efficiency .................................................................................................26
4.4 Warehouse .............................................................................................................27
4.5 Information systems ...............................................................................................28
4.5.1 SAP .................................................................................................................28
4.5.2 Production follow-up tool .................................................................................28
4.5.3 MES ................................................................................................................28
4.5.4 Warehouse Management System (WMS) .......................................................29
4.5.5 Business Intelligence software (BI) ..................................................................29
4.6 Inventory Control ....................................................................................................29
4.6.1 Batch Size .......................................................................................................29
4.6.2 Service Level...................................................................................................29
4.6.3 Safety stock ....................................................................................................30
4.7 Activities in the Planning Department .....................................................................31
4.7.1 Operative planning process .............................................................................31
4.7.2 Stock building ..................................................................................................32
4.7.3 Cycle planning of SKUs ...................................................................................33
4.7.4 Sales and Operations Planning at the Company .............................................33
5 Analysis .........................................................................................................................37
vi
5.1 Mathematical Lot sizing ..........................................................................................37
5.1.1 EOQ ................................................................................................................37
5.1.2 Wagner-Whitin ................................................................................................38
5.1.3 Silver Meal ......................................................................................................38
5.1.4 Chosen Model .................................................................................................38
5.2 Changeover Cost ...................................................................................................39
5.2.1 Changeover Times ..........................................................................................39
5.2.2 Fixed changeover cost ....................................................................................40
5.2.3 Variable Changeover Cost ..............................................................................40
5.2.4 Total changeover cost .....................................................................................40
5.2.5 Outcome .........................................................................................................41
5.3 Holding cost ...........................................................................................................41
5.3.1 Holding cost in todayβs operations ...................................................................42
5.3.2 Holding cost for an extended internal warehouse ............................................43
5.4 Demand .................................................................................................................43
5.5 Constraints in Processing .......................................................................................44
5.6 Statistical analysis related to Perished Goods ........................................................45
5.6.1 Maximum Batch Size .......................................................................................45
5.6.2 Expected volume of perished goods ................................................................47
5.6.3 Discussion of approaches ...............................................................................48
5.7 Resulting batch sizes from the model .....................................................................48
5.8 Safety Stock ...........................................................................................................51
5.8.1 Implication of current setup .............................................................................51
5.8.2 A new suggestion ............................................................................................53
5.9 Effects on finished goods inventory ........................................................................56
5.10 Effects on production ..............................................................................................57
5.11 Cycle planning ........................................................................................................59
5.12 Summary ................................................................................................................60
6 Model Outline ................................................................................................................63
6.1 Application of the Model .........................................................................................63
6.2 Model procedure ....................................................................................................63
6.3 Model procedure to evaluate effects. ......................................................................65
6.4 Input Data ..............................................................................................................65
7 Discussion .....................................................................................................................67
7.1 Sensitivity analysis .................................................................................................67
7.2 Scientific contribution .............................................................................................68
vii
7.3 Areas for future improvement .................................................................................68
8 Summary and Conclusions ............................................................................................69
9 Recommendations ........................................................................................................71
10 References ................................................................................................................73
viii
List of Figures Figure 1: The balanced approach to research strategy (Kotzab & Westhaus, 2005, p.20) ..... 6
Figure 2: The MRP2 hierarchy (Hopp & Spearman, 2001, p.136). ........................................12
Figure 3: Level of stock in the system as assumed in EOQ-model (AxΓ€ter, 2006) ................13
Figure 4: Example of the wagner-whitin algorithm at work (AxΓ€ter, 2006, p.65). ...................15
Figure 5. (R,Q) Policy (AxΓ€ter, 2006, p.50) ...........................................................................18
Figure 6: The companyβs supply chain in Sweden ................................................................23
Figure 7: Activity distribution for the open time of line X. .......................................................27
Figure 8 stock on hand at the warehouses dated back to January 1, 2017. ..........................28
Figure 9 The operative planning process ..............................................................................31
Figure 10: Demand of SKUs produced by line Y throughout the year, and the capacity of the
line. ......................................................................................................................................32
Figure 11: The S&OP process at the company. ....................................................................34
Figure 12. Demand for the SKUs on the four lines throughout the year. ...............................44
Figure 13 Histogram of FE for a SKU. ..................................................................................45
Figure 14 illustration of risk for perished goods.....................................................................46
Figure 15. Average batch size per recipe-group. ..................................................................49
Figure 16 Average batch sizes on the four studied lines. ......................................................50
Figure 17 cost analysis when deviating from optimum batch size .........................................51
Figure 18: Histogram of yield loss in percent for Line Y, a negative yield loss means the
produced quantity was larger than the planned. ...................................................................54
Figure 19: Safety stock for new suggestion and Current setup .............................................56
Figure 20 Contributions of average stock on hand from the studied lines. ............................57
Figure 21: Changes is production time and changeover times at the lines. ...........................59
Figure 22: Tiers of suggested model ....................................................................................63
Figure 23: Flowchart of working model procedure. ...............................................................64
Figure 24. Illustration of selection of possible batch sizes. ....................................................65
Figure 25: The different input categories of the model ..........................................................66
ix
List of Tables Table 1: Opening hours in production during a week. ...........................................................24
Table 2: Average production fulfillment during the last 4 years for the four studied production
lines. .....................................................................................................................................25
Table 3: Average change over times of different recipe groups on one line during 2017 in
minutes.................................................................................................................................39
Table 4: Average changeover times of different SKUs in a recipe group during 2017 in
minutes.................................................................................................................................40
Table 5: The Changeover cost for all recipes in SEK. Each cell in the columns represent one
of the recipes of the line. ......................................................................................................41
Table 6: Consequence of constraints on batch size ..............................................................44
Table 7 results of MAXQ and expected perishable goods for a selection of SKUs. ...............47
Table 8. Average batch sizes for a selection of SKUs...........................................................49
Table 9: Last six months service level for the 10 SKUs with highest sales volume, as
observed, and the target βstock service levelβ. ......................................................................52
Table 10: Mean and standard deviation of yield losses for the lines in this study, note that it is
displayed in units of percent. ................................................................................................55
Table 11. Calculated parameters for the selection of articles ................................................58
Table 12. Production time per week ....................................................................................58
Table 13: The Cycle-planning helper. ...................................................................................60
Table 14. Data aggregated to evaluate effects on production and finished goods inventory for
a selection of SKUs across the 4 lines included in the report. ...............................................65
1
1 Introduction
During the introduction the reader will be introduced to the company and their current
situation. The problem will be described, a clear purpose of this thesis, and its delimitations,
will be stated.
1.1 Background
The beverage industry has ancient roots. For example, the procedure of refining water, malt,
hops and yeast into beer, called Brewing is a complicated process that have been developed
by humans for more than 7000 years. (Nelson, 2005)
The project was performed at the request of a company that manufactures beverages, at
their production facility in Sweden. The facility produces a multitude of different beverages
and packages them to be sold. The company possesses a vast array of brand that are both
internationally and locally known. The company wishes to remain anonymous, and shall in
this thesis be referred to as βThe companyβ. The names of the production lines and the
articles have also been altered in this thesis.
This thesis concerns the manufacturing unit in Sweden which produce drinks for the Swedish
market. In total, around 400 unique products are produced in the facility at this time.
1.2 Problem Description
The company currently experience difficulties in the decision-making process regarding
ordering quantities along their supply chain. The planning department is responsible for
determining the produced batch sizes, but the decisions affect the various departments
throughout the supply chain in different ways depending on which KPIs (Key Performance
Indicators) the department is evaluated upon. Therefore, the batch sizes in the production
are a topic of much interest for the entities in the supply chain and various opinions related to
them exist.
Several problematic areas that might be affected by the batch sizes exist. The warehouse
management team brings attention to the fact that 40-60% of the companyβs finished goods
inventory is stored at expensive external warehouses, to which inventory must be
transported. In turn, the production management highlights the low equipment efficiency
shown on the production lines and the resulting cost of sourcing goods that cannot be
produced on site due to lack of capacity. Sourcing of finished goods and the cost of external
warehouses are considered by the departments to be major unnecessary cost drivers.
The planning department currently have an ambition to decrease the total stock and to create
good conditions for the production team, to increase their equipment efficiency by reducing
the number of change overs. They think this can be done by enhancing the procedure of
determining batch sizes in production, an effort that is complicated by the complexity of the
companyβs large product portfolio and constraints in their production process, as well as the
2
perishability of the finished goods. The planning team is currently guided by SAP to handle
the production scheduling of the production lines. SAP suggests a preliminary production
schedule with batches that aim to satisfy the demand from the customers, but does not take
the costs driven by the batches, into account.
To support the planning team in the batch size determination, as well as in negotiations with
the different functions, a model that quantifies the costs associated with the batch sizes have
been requested. To increase the understanding of the impacts of decisions, the model is
requested to be capable of evaluating the effect of changes to the finished goods inventory
and the production
1.3 Purpose
The purpose of this project is to create a quantitative model that takes relevant costs and
variables into account when determining the production batch sizes. The objective is also to
evaluate the impact the model would have on finished goods inventory and the production
capacity.
1.4 Delimitations
To be able to perform the project in the limited time frame, the scope is narrowed down.
Firstly, only one of the companyβs production facilities is included. Therefore, the scope of the
project has been limited to the supply chain and the operations related to this production unit.
The ambition to create a model which can be used in the planning process for most products
have because of the limited time frame been tested on four of the production lines.
3
2 Methodology
Appropriate research methodology is crucial to clarify how the project will be carried out and
for the quality assurance. However, the purpose of the methodology is not to dictate how the
work will be executed but rather guide the process of acquiring knowledge from the problem
formulation. (HΓΆst, et al., 2006). In this chapter, several key aspects of the methodology will
be presented. Motivations are given for the chosen methodology and how quality is assured.
2.1 Research purpose
A methodology can have different purposes depending on the goals and characteristics of
the project (HΓΆst, et al., 2006). Four different types of purposes are presented by Runesson
and HΓΆst (2009), namely exploratory, descriptive, explanatory and improving. The research
purpose depends on the knowledge of the studied phenomenon. Exploratory research aims
to explore and develop an understanding of the phenomenon. With greater knowledge of the
phenomenon, a descriptive research purpose aspires to describe what is happening.
Explanatory research intends to explain the phenomenon. An improving research purpose
develop a solution which solves a problem. Thus, the different purposes represent the level
of understanding of the problem which increases from little knowledge in an exploratory
research purpose to profound knowledge in an improving research purpose (Runesson &
HΓΆst, 2009).
2.2 Research Design
A suitable research design must be aligned with the research purpose. Examples of ways to
design a research study are through case studies and modelling (HΓΆst, et al., 2006). Kotzab
and Westhaus (2005) use the phrase research strategy and outline case studies and
modelling from a supply chain perspective. Christer Karlsson (2016) also explains these
strategies from an operations management perspective.
2.2.1 Company case study
Projects which are set out to solve a problem experienced in a manufacturing industry are by
its nature a study of a particular case and thus the design of the methods are considered
flexible. (HΓΆst, et al., 2006) In this context, flexible means that the questions asked, and the
alignment of the study can be altered during the project itself. These studies can include both
quantitative and qualitative evidence. They also benefit from multiple sources for these
evidence, as well as from a previously set theoretical framework. (Yin, 2014)
2.2.2 Modelling
A model is an abstraction of the reality where un-relevant aspects of the phenomenon are
disregarded (HΓΆst, et al., 2006). Modelling of supply chains can relate to quantitative
methods such as systems dynamics, agent-based simulation, object-oriented modelling,
discrete event simulation, stochastic modelling, optimization problems and queuing networks
(Kotzab & Westhaus, 2005). These methods are applied to study how uncertainty and
inventory quantities affect the performance of the supply chain (Kotzab & Westhaus, 2005).
4
2.3 Research Techniques
There are several different techniques that can be used for collecting data when studying a
particular case. HΓΆst, Regnell and Runesson (2006) especially mention three common
techniques, which can be conducted in several ways. These are Interviews, Observations
and Archive analysis.
2.4 Problem Description
The company currently experience difficulties in the decision-making process regarding order
quantities along their supply chain. The planning department is responsible for determining
the batch sizes used in production, but the decisions affect the various departments
throughout the supply chain in different ways depending on which KPIs (Key Performance
Indicators) the department is evaluated upon. Therefore, the batch sizes in the production
facility is a topic of much interest for all the different entities in the supply chain.
Several problematic areas that might be affected by the batch sizes exist. The warehouse
management team brings attention to the fact that 40-60% of the companyβs finished goods
inventory is stored at expensive external warehouses, to which inventory must be
transported. In turn, the production management highlights the low equipment efficiency
seen in some of the production lines and the resulting cost of sourcing goods that cannot be
produced on site due to lack of capacity. Sourcing of finished goods and the cost of external
warehouses are considered by the departments to be major βunnecessaryβ cost drivers.
The planning department currently have an ambition to decrease the total stock and to create
good conditions for the production team, to increase their equipment efficiency by reducing
the number of change overs. They think this can be done by enhancing the procedure of
determining batch sizes in production, an effort that is complicated by the complexity of the
companyβs large product portfolio and constraints in their production process, as well as the
perishability of the finished goods. The planning team is currently guided by SAP to handle
the production scheduling of the production lines. SAP suggests a preliminary production
schedule with batches that aim to satisfy the demand from the customers, but does not take
the costs driven by the batches, into account.
To support the planning team in the batch size determination, as well as in negotiations with
the different functions, a model that quantifies the costs associated with the batch sizes have
been requested. To increase the understanding of the impacts of decisions, the model is
requested to be capable of evaluating the effect of changes to the finished goods inventory
and the production.
2.4.1 Interviews
Interviews can be a powerful tool to gain a personβs knowledge from the current setup and
configuration of the system. An interview can be conducted in several ways, the number of
which is different in various literature. Cohen, Manion and Morrison (2000) specifies four
distinct types of interviews, each with their strengths and weaknesses.
5
An Informal conversational interview is similar to a natural conversation between the
participating parties and follows no beforehand set agenda. The strength of this is that it is
flexible in its nature and the topic emerges and evolves as the interview progresses. On the
other hand, it has the weakness of being unreliable as the chance for unbiased answers and
leading questions increase.
Interviews conducted with a guided approach or with standardized questions are both more
systematically done and makes the data collection more efficient and robust. It is also easier
to review the plan of the interviews. The negative side of these approaches are that take a lot
of resources to conduct. The guide approach is presented by Yin (2013) as a semi structured
interview.
Lastly, closed quantitative interviews are essentially questionnaires with fixed answers,
suitable for quick interviews and analysis. The primary weakness is that the interviewer is
essentially forcing the participant to provide the βleast wrongβ alternative.
2.4.2 Observations
Cohen, Manion and Morrison (2000) argue that observations are conducted on a continuous
spectrum ranging from a highly structured to a semi-structured ending in an unstructured
approach. Simplified, a structured approach is based on a hypothesis and uses the
observation to either reject or confirm it while an unstructured approach aims to be
exploratory (Cohen, et al., 2000).
2.4.3 Archive analysis
Archive analysis is the activity of examining historical data gathered for other purposes than
those in the actual project (HΓΆst, et al., 2006). Historical research is also introduced by
Cohen, Manion and Morrison (2000), saying that βHistorical research has been defined as
the systematic and objective location, evaluation and synthesis of evidence in order to
establish facts and draw conclusions about past eventsβ, originally stated by Borg (1963).
The definition of Archive analysis from HΓΆst, Regnell and Runesson (2006) is closely in line
with what in research commonly is called secondary data. In contrast to secondary data,
primary data is information collected for the specific research project and its defined purpose
(Bryman & Bell, 2011). As a result primary data is generally resistant to uncontrollable bias.
As with the other research methods, historical data has strengths and weaknesses. The main
strength is that current problems can be solved by using data from former events that have
already been recorded (Cohen, et al., 2000).
Cohen, Manion and Morrison (2000) argue that the weakness of using historical data is the
vulnerability to vague problem descriptions. It is important to define the problem precisely
and to avoid using broad descriptions. As support to this statement they use a quote from
Best (1970) saying that βThe experienced historian realizes that research must be a
penetrating analysis of a limited problem, rather than the superficial examination of a broad
area. The weapon of research is the rifle not the shotgunβ. The conclusion is that for relevant
analysis of historical data, the starting point or the problem description must be explicit and
precise.
6
Related to this project, data from former events have been obtained from the companyβs IT-
systems.
2.5 Research Approach
Deductive research and inductive research represent two perspectives of how the research
are conducted (Bryman & Bell, 2011). The deductive perspective sees the relationship
between theory and research praxis as testing of ideas developed from theory. The inductive
perspective is the other way around, where theory is generated from the research praxis. A
third way to conduct research is called the abductive approach which suggests an iterative
process between deductive and inductive research (Freytag & Young, 2018).
2.6 Research Strategy
Traditionally in a business context, there has been a distinction between qualitative- and
quantitative research. The most obvious difference is the associations between qualitative
research and words, and the association between quantitative research and numbers
(Bryman & Bell, 2011). Quantitative research puts effort into analysing procedures and
descriptions of the studied phenomenon. Questionnaires, interviews and or documents are
common ways to conduct qualitative research. Quantitative research use mathematical or
statistical methods to analyse the gathered data. Field studies associated with quantitative
research include surveys or experiments (Bryman & Bell, 2011).
Kotzab & Westhaus (2005) point out that historically, research in the context of logistics and
supply chain management mainly has been deductive and typically been using quantitative
methods. Therefore, the need for inductive research, especially the need for qualitative
methods is identified in this environment. A suggested strategy to solve this is the balanced
approach which incorporates both qualitative and quantitative research in an iterative way.
The strategy is illustrated in Figure 1 below.
Figure 1: The balanced approach to research strategy (Kotzab & Westhaus, 2005, p.20)
7
Kotzab and Westhaus (2005) explain that the applicability of the balanced approach depends
on the initial understanding of the problem. If the level of understanding is low, the suggested
approach is to start with qualitative methods and further on use the established knowledge to
develop relevant quantitative approaches. If a well-known phenomenon is studied, the
suggested approach is to start with the quantitative approach to gain a deeper understanding
of the more complex aspects of the problem, from where a qualitative approach could be
used to explain it.
2.7 Quality Assurance
Several components need to be accounted for to achieve a trustworthy quality assurance of
a thesis. HΓΆst, Regnell and Runesson (2006) accounts for three categories:
2.7.1 Reliability
Reliability can in quantitative research be said to be equivalent to consistency and
reproducibility over time, over instruments and over groups of correspondents. (Cohen, et al.,
2000) Three different types of reliability are stability, equivalence and internal consistency.
2.7.2 Validity
Cohen, Manion and Morrison (2000) state that validity should not be absolute but rather as βa
matter of degreeβ. Thus, perfection in validity is not achievable but aiming for a high degree
of validity in a thesis is important. HΓΆst, Regnell and Runesson (2006) further comments that
validity is a matter of how well the data gathered is connected to what is intended to be
measured.
2.7.3 Representativeness
Representativeness refers to the possibility to generalize the research material. HΓΆst,
Regnell and Runesson argue that strictly speaking, case studies are not generalizable in a
broader context but can with the help of coinciding parameters of different cases be
applicable in similar studies. Therefore, a pronounced description of the situation for the
investigated case can increase the representativeness of the thesis. (HΓΆst, et al., 2006)
2.8 Chosen methodology
This section summarises the chapter by presenting the chosen methodology and arguing for
its quality.
2.8.1 Used Methodology
As previously mentioned, different types of research purposes are associated with different
levels of understanding of the problem. Therefore, the purpose of the earlier stages of the
project are exploratory while the purpose of the later stages are descriptive, explanatory and
even in some respects improving since the purpose is to create a model to guide future
decisions. To enable such outcome, one first need to understand the problem, which is the
purpose of explanatory research. The purpose of developing a model which represent the
8
reality is closely in line with descriptive and explanatory research. Since the projectβs purpose
is to develop a quantitative model which evaluates effects of changes, the most heavily
emphasised research purpose is explanatory and improving.
The project take place in a business environment. Therefore, one used research design in
the project is a study of a particular case. Every organisation operates under its specific
conditions which limits the general representativeness. By presenting the specific conditions
in this study, the representativeness is improved and argued to be high for organisations with
similar circumstances.
The other used design is modelling, since one of the main tasks in the project is to develop a
quantitative model. The process of developing the model is described in the next section,
working procedure.
The chosen strategy is the balanced approach which incorporates both qualitative- and
quantitative research strategies. The project starts with qualitative methods such as informal
and formal interviews, to develop a deeper understanding of the problem. The knowledge is
then extended by quantitative research. In this way the validity of the quantitative research is
argued to be high, since the qualitative interviews and observations have pointed out
relevant data to use. In the balanced approach both inductive and deductive research
approaches are used. For that reason, an abductive research approach is taken where ideas
are developed and tested in an iterative way.
Suitable research techniques to gather data and information for this project include
Interviews, Observations and Archive analysis. These are used to build a solid understanding
of the problem, as well as for validation, which is especially important in a complex
environment where a holistic view is needed. Both informal conversations and guided
interviews have been conducted. The informal interviews are used to gather relevant
information to understand the nature of the problem, without affecting the interviewee with
formal questions. The guided interviews are used to test and validate the information. Also,
data from the companyβs IT-systems are used to test and validate the information, by
confirming or contradicting the given information. To rely on established methods improves
the validity in the study. The data from the archive analysis is argued to be of high validity
since relevant and accurate data are obtained from the companyβs IT-systems. The data in
the IT-systems have not been modified and are thus considered to be unbiased data with
high reliability and validity.
As the work is made in an ever-changing organisation, consistent results cannot be
guaranteed after time have passed. This is partly circumvented in the data gathering part of
the thesis by delimiting data recorded prior to major changes in the companyβs operation. For
example, a substantial change in the process of a line will result in the removal of the data
from before that change in the analysis.
9
2.9 Working procedure
Hillier and Lieberman (2010) suggest a working procedure that can be divided into the six steps presented below.
1. Defining the Problem and Gathering Data 2. Formulating a Mathematical Model 3. Deriving Solutions from the Model 4. Testing the Model 5. Preparing to Apply the Model 6. Implementation
The procedure has been modified to fit this project and broken down to sub-steps to further guide the work. Because of the time-limitation s of the project, the mathematical model is less comprehensive than those mentioned in Hillier and Liebermann (2010). Therefore step 2, 3 and 4 are merged into one step: step 2. Developing a quantitative model. The model is continuously built, validated and tested which suggest an iterative process of the three sub-steps. Giving the time constraints for this project no implementation of the results and little effort will be put into preparing the model for continuous use for the employees. The updated procedure is structured according to the steps below.
1. Defining the Problem and Gathering Data
1.1. Mapping the supply chain. 1.2. Evaluate and validate the process map. 1.3. Identify crucial variables to include in the model. 1.4. Identify data required to build framework of the model 1.5. Collect, clean and validate data.
2. Formulating a mathematical model
2.1. Developing the model and deriving solutions 2.2. Validate the model and its solutions 2.3. Test the model
10
11
3 Theoretical Framework
To provide a sufficient base of knowledge for the reader to follow the later chapters in the
report, this chapter is dedicated to present relevant theory.
The chapter starts by presenting theory related to management of business and business
processes to provide knowledge for the context of the problem. Thereafter, the theory used
to develop the quantitative model is presented.
3.1 Strategic levels of organisations
Literature often refer to three strategic levels of a business plan, namely strategic, tactical
and operational which represent different hierarchical levels in the organisation (Johnson, et
al., 2015). The strategic level is the long-range business plan which include questions such
as what we do and who we do it for. A tactical plan includes actions for how a specific
department contributes to the strategic plan. An operational plan ties to the tactical plan by
converting the plan to activities in the department (Johnson, et al., 2015). Hill and Hill (2009)
use the terminology Corporate-level, Business unit-level and Functional-level to describe
levels of strategy. They highlight the importance of the linkage between functional strategies
and business unit strategy. The authors emphasise that the functional strategies should be
developed together towards the same goals defined by the business unit strategy (Hill & Hill,
2009). They further explain that for many businesses the strategic collaboration between the
marketing department and production is especially troublesome. A marketing departmentβs
purpose is to provide high customer service for criterions such as customization of products,
volume and lead times since it generates sales. While performing high on these parameters
is equivalent with costs for the operations which therefore has a conflicting attitude to such
decisions. The discussion is shaped by strategic decisions such as investments in resources
and priority of future revenues of growth (Hill & Hill, 2009).
3.2 Sales and Operations Planning
Sales and operations planning (S&OP) is a tactical business process which links the
corporate strategy with the daily operative processes by balancing the supply with the
demand (Grimson & Pyke, 2007). The S&OP process is typically based around the five
steps; Data Gathering, Demand Planning, Supply Planning, Preparation-meting, Executive
Meeting (Wallace & Stahl, 2008).
Essential for the result is the cross-functional collaboration between the departments. To
reach a balance, it is necessary to coordinate the functionsβ activities (Grimson & Pyke,
2007). To do so, functional silos must be broken down and managers must work towards a
common goal (Grimson & Pyke, 2007).
Grimson and Pyke (2007) pointed out that so far, the development of the S&OP-method are
shaped by the industry rather than the academia, although academia are constantly working
to fill the gap. Noroozi and Wikner (2017) have pointed out that particularly the
implementation of S&OP in the process industry has not received much attention in the
literature, compared to the discrete manufacturing industry. Grimson and Pyke (2007)
12
addressed the gab by providing a framework to determine the maturity level of the S&OP-
process in the company.
3.3 Enterprise Resource Planning
Enterprise Resource Planning (ERP) is the current embodiment of the material requirements
planning (MRP) system that was introduced in the 1960s and then popularized 1972 when
the American Production and Inventory Control Society launched their βMRP Crusadeβ
campaign (Hopp & Spearman, 2001). The basic function of MRP is to plan material
requirements by coordinating orders within the plant with orders outside the plant (Hopp &
Spearman, 2001). MRPβs main task is therefore to schedule jobs and purchase orders to
satisfy material requirements downstream, generated by an external demand. Manufacturing
resource planning (MRP II) is an extension of MRP that include demand management,
forecasting, capacity planning, master production scheduling, rough-cut capacity planning,
capacity requirements planning, dispatching, and input/output control. The functions are
explained in a hierarchy illustrated in Figure 2 below.
Figure 2: The MRP2 hierarchy (Hopp & Spearman, 2001, p.136).
The long-range production planning has a time range from around six months to, two to four
years and the aggregated production planning are typically made for part families. (Hopp &
Spearman, 2001)
13
At the intermediate-range planning, the master production scheduler takes the demand and
the available capacity into account to create an anticipated production schedule at the
highest level of planning detail. The material requirement planning coordinates the
requirements of material for the orders to create a job pool from where jobs could be
released into production in the short-term control (Hopp & Spearman, 2001).
3.4 Lot Sizing
Lot sizing is a major driver for both costs and customer service in a supply chain and the
topic have been extensively studied during the last century. (Hosang, et al., 2007) The
problem has been found to be difficult to solve and Arkin et al (1989) showed that the
problem is NP-hard for a general network topology which makes it especially complex to
solve for larger supply-chains.
This have made researchers move away from trying to solve the lot sizing problem generally
and instead much focus is being put on restricted models as well as heuristic methods.
(Hosang, et al., 2007)
This section will present some of these models and heuristics (showing assumptions and
limitations) for analysis in later chapters.
3.4.1 The Economic Order Quantity
As one of the earliest and most well-known approaches to inventory management, the
economic order quantity (EOQ) is one of the simplest way to determine a cost minimum for
operations. (Harris, 1913) (Hopp & Spearman, 2001)
The EOQ model rest on assumptions that concern most parts of the supply chain. The
production rate is assumed to be instantaneous, delivery is immediate and demand is
assumed to be deterministic and constant over time demand. A changeover induces a fixed
cost and keeping inventory in stock brings a constant holding cost. (Hopp & Spearman,
2001)
A consequence of these assumptions is that the average stock is the maximum stock Q
divided by two. This implies, as visualised in Figure 3, that the average stock level is π
2.
Figure 3: Level of stock in the system as assumed in EOQ-model (AxΓ€ter, 2006)
14
Following AxsΓ€ter (2006, page 52) a quick derivation of the EOQ-formula is presented below.
For a more extensive derivation, deeper understanding and proof of convexity we refer to
Hopp & Spearman (2001, page 49).
Using the following notations:
C = Cost per time unit h = holding cost per unit and time unit, A = ordering or changeover cost, d = demand per time unit, Q = batch quantity The relevant costs related to the ordering cost are the holding cost and the changeover
costs. The average holding cost per time unit is approximated to the average stock times the
holding cost per unit. The average changeover cost per time unit is simply the number of
changeovers per time unit, times the fixed cost of changeover. This gives:
πΆ =π
2β β +
π
πβ π΄ (1)
To find the optimal batch quantity, the cost function is differentiated with regards to Q and set
equal 0.
ππΆ
ππ=
β
2β
π
π2β π΄ = 0 (2)
Solving for Q the optimal order quantity is obtained.
πβ = β2 β π΄ β π
β (3)
Inserting the optimal order quantity in the cost function the following results are obtained:
πΆβ = βπ΄πβ
2+ β
π΄πβ
2= β2π΄πβ (4)
Combining equation 1 and 4 we obtain
πΆ
πΆβ=
π
2β
β
2π΄π+
1
2πβ
2π΄π
β=
1
2(
π
πβ+
πβ
π) (5)
From (5), AxsΓ€ter (2006) concludes that a 50% increase or decrease from the optimal order quantity only increase the cost by about 8%. AxsΓ€ter (2006) also notes that the cost parameters are even less sensitive. Using an ordering cost 50% higher than the real cost only impacts the final cost with 2%.
15
3.4.2 Wagner-Whitin
Another, more complicated, way to incorporate the time-varying demand in the calculation is
the usage of the Wagner-Whitin algorithm. Again, time is not modelled as continuous and
infinite but rather as a finite number of discrete time periods. The holding cost and
changeover cost is still constant over time. The same notations as AxsΓ€ter (2006) is used.
π = ππ’ππππ ππ πππππππ
ππ = π·πππππ ππ ππππππ π
π΄ = ππππππππ πππ π‘
β = βππππππ πππ π‘ πππ π‘πππ π’πππ‘
Wagner-Whitins optimal solution hold two properties, as presented by AxsΓ€ter (2006, page
63):
1. A replenishment must always cover the demand in an integer number of consecutive
periods.
2. The holding costs for a period demand should never exceed the ordering cost.
The objective of the algorithm is to minimize the total cost of the ordering cost and holding
cost for all periods T. Since the demand is no longer constant during all periods neither is the
optimal ordering quantity. AxsΓ€ter (2006) give an example, shown in Figure 4, of how this
computation is made for A = 300 and h = 1 per unit of time with a timeframe of 10 periods.
Figure 4: Example of the wagner-whitin algorithm at work (AxΓ€ter, 2006, p.65).
As shown, every feasible solution, following the two optimal solution properties have been
computed for each time period. The algorithm then selects the solution with the least total
cost as the optimal solution.
3.4.3 Silver-Meal
A well-known method is to use the Silver-Meal heuristic. (Silver & Meal, 1973). In this
heuristic, a new delivery is chosen the time period where the average cost per period
increase for the first time. Using the same example as before, AxΓ€ters (2006, 66) explain
how the heuristic work. Below the period cost for deliveries that cover 2, 3β¦ periods are
presented.
2 periods (300+60)/2 = 180 < 300,
3 periods (300 + 60 + 2 * 90)/3 = 180 < 180,
16
4 periods (300 + 60 + 2 β’ 90 + 3 * 70)/4 = 187.5 > 180, which means a new delivery in
period 4.
For a full through explanation of the heuristic we refer to AxΓ€ter (2006, 66).
3.5 Critical Variables
The above models are all subject to limitations, and all require calculation of input
parameters A (changeover cost), h (holding cost for period t) and d (demand over period t).
Vital to observe when using the holding cost and changeover cost to calculate an optimal
ordering quantity is to only include costs that are directly affected by the ordering quantity
decision. (AxΓ€ter, 2006)
3.5.1 Holding Cost
The holding cost, h, is the cost for keeping one unit in stock, one unit of time. According to
Berling (2005), the holding cost can be divided in four main cost components.
β’ Capital cost
β’ Inventory service cost
β’ Storage space cost
β’ Inventory risk cost
The capital cost is essentially tied up to the expectations of the companyβs stakeholders.
While the capital is tied up in inventory, the chance is high that it will not grow in value at the
same rate as if it were invested elsewhere. Stakeholders often accept lower return on
invested capital when the risk is low and consequently require a higher return of high risks
investments. Berling (2005) compare this to the stock market where it is commonly accepted
that high return stocks carry higher risks, while for example index funds generally generate
lower returns while also carrying a reduced risk.
The Inventory service cost, the Storage space cost and the Inventory risk cost can often be
consolidated and are then referred to as out-of-pocket costs. (Berling, 2005). Particularly
when outsourcing storage to a third-party firm. Observe that the inventory risk cost is the cost
associated to physical risk of keeping the goods in stock and not the financial risk of doing
so.
In short, the out-of-pocket holding cost consists of costs connected to the physical storing of
the units such as rent and transportation, tax and insurance together with the cost of risk (i.e.
the risk that the goods cannot be sold at full price due to circumstances connected to the
time stored).
17
3.5.2 Activity Based Costing
The method of Activity Based Costing originated from price calculations for products, based
on the cost of producing them (SkΓ€rvad & Olsson, 2005). Costs related to the price are of
both direct- and indirect nature. One example of a direct costs are material cost to produce
the product. Examples of indirect cost are cost such as planning the production (SkΓ€rvad &
Olsson, 2005).
The essential in the ABC-method is how the indirect costs are allocated to certain activities.
The costs related to the activity are allocated based on specific cost drivers. Berling (2005)
concludes that the holding cost can be derived from the used amount of the resource which
is derived from the cost driver ππ, and the activity cost π which is the marginal increase of the
average cost with respect to the mean output level.
βπ = ππ β π (6)
3.5.3 Changeover Cost
The changeover cost (A), also consist of different elements. According to Berling (2005)
these often include personnel and equipment costs, as well as the reduction in capacity
associated with smaller batches. It can be concluded that the changeover cost is dependent
on several company and machinery specific factors that will be further discussed later in the
report.
Changeover costs can increase significantly if an expensive, capacity constrained, machine
needs to pause during the setup. (AxΓ€ter, 2006)
3.5.4 Shortage Cost
The shortage cost is the cost associated with not being able to meet the demand from a
customer in the supply chain on time. A customer can be the end-customer but also for
example another step in the production process.
Shortage costs can in the short range be easily quantified, as an incoming customer order
that is rejected is a direct loss in sales. In the long run however, a dissatisfied customer
might bring their business elsewhere or affect other customers, leading to lost future sales,
this is harder to quantify (Berling, 2005).
3.6 (R, Q) Policy
Simple inventory policies to control the inventory have been developed to decide when and
how much to order. One of the most widely used policies is the (R, Q) Policy. Inventory
systems can be designed so that the inventory position is continuously monitored, denoted
continuous review. They can also be reviewed at certain times, denoted periodic review
(AxΓ€ter, 2006).
Crucial variables are:
πΏ = πΏπππ π‘πππ
π = πππ£πππ€ ππππππ, π. π, π‘βπ π‘πππ πππ‘πππ£ππ πππ‘π€πππ πππ£πππ€π
18
The decision of when and how much to order should be based on the stock situation,
demand and cost parameters (AxΓ€ter, 2006). Notations used by AxΓ€ter (2006) are:
β’ outstanding orders, defined as orders made that have not yet arrived
β’ backorders, defined as units that have been demanded but not yet delivered
πππ£πππ‘πππ¦ πππ ππ‘πππ = π π‘πππ ππ βπππ + ππ’π‘π π‘ππππππ ππππππ β ππππππππππ
πππ£πππ‘πππ¦ πππ£ππ = π π‘πππ ππ βπππ β ππππππππππ
In an (R,Q) Policy, an order of Q units will be triggered when the inventory position declines
to R or below. The maximum inventory position for this system are thus R+Q (AxΓ€ter, 2006).
How a periodically reviewed (R,Q) policy operates are presented below in Figure 5.
Figure 5. (R,Q) Policy (AxΓ€ter, 2006, p.50)
3.7 Service Levels and Safety Stocks
In a (R, Q) system, a common procedure to determine the required safety stock is to base it
on achieving a predefined service level. AxΓ€ter (2006) present three definitions of service
levels:
π1 = probability of no stockout per order cycle,
π2 = "fill rate" β fraction of demand that can be satisfied immediately from stock on hand. π3 = "ready rate" β fraction of time with positive stock on hand. Worth noticing is that if the demand is continuous, S2 and S3 are equivalent (AxΓ€ter, 2006).
S1 is usually used in combination with continuous review models and continuous demand. A
disadvantage with using S1 for inventory control is that it does not take the batch size (Q)
into account. In a (R, Q) policy the problem of determining S1 is about choosing R, such that
there is a certain specified probability S1 for the demand during the lead time to be lower
than R. With the assumption that the demand during the lead time is normally distributed with
average mean πβ² and standard deviation πβ², the problem can be formulated as:
19
π1 = π(π·(πΏ) β€ π ) = π (π β πβ²
πβ² ) = π (ππ
πβ²) , (7)
where the safety stock SS is defined as R-πβ² and π is the cumulative distribution for the
normal distribution (AxΓ€ter, 2006).
For a (R, Q) policy and continuous normally distributed demand S2 and S3 is the probability
of positive stock, which can be obtained from (8) below (AxΓ€ter, 2006).
π2 = π3 = 1 β πΉ(0) = 1 βπβ²
πβ [πΊ (
ππ
πβ²) β πΊ (
ππ + π
πβ²)] (8)
Where G is defined as:
πΊ(π₯) = β« (π£ β π₯)π(π£)ππ£ = π(π₯) β π₯(1 β π(π₯))β
π₯
(9)
Note that πΊβ²(π£) = 1 β π(π£).
In a situation where safety stock is used, the average stock on hand presented in section
3.4.1 (Economic Order Quantity) can be approximated as: (AxΓ€ter, 2006)
ππ£πππππ π π‘πππ ππ βπππ = ππ +π
2
This is evident, since the average stock without the safety stock is Q/2 and the average
variation of the demand is 0 due to the normality of the demand.
3.8 Yield loss
Yield loss in production is volume lost due to unplanned events in the process. These events
include everything from machine malfunction to lack of raw material.
Yield loss in production can be modeled, for example, using a stochastic proportional yield
model where a certain quotient of the planned volume Y, π β [0,1] is produced such as the
resulting output is the product of the planned volume Y and the quotient Z. The stochastic
quotient Z belongs to some arbitrary distribution. (Sonntag, 2017)
3.9 Statistical Theory
This section provides the reader with the basic statistics theory used in the analysis section.
3.9.1 Linear combinations of stochastic variables
The normal distribution has the property that the sum of independent normally distributed
stochastic variables is normally distributed. This has the following effect if X and Y are two
normally distributed stochastic variables (Blom, et al., 2005)
π β π(ππ₯ , ππ₯)
20
π β π(ππ, ππ)
π + π β π(ππ + ππ, βππ2 + ππ
2)
3.9.2 Statistical fitting
Processes are rarely deterministic. A standard procedure for statistical distribution fitting can
be described as follows (Laguna & Marklund, 2013):
Phase 1. Identify appropriate distribution family by graphically presenting the data.
Phase 2. Estimate distribution parameters based on the distribution family to develop a
hypothesis for a specific distribution.
Phase 3. Perform a statistical goodness-of-fit test to investigate if the hypothesis may be
rejected. These phases continue until a hypothesis for a distribution cannot be
rejected. If no well-known distribution family is appropriate, an empirical
distribution may be used.
To manually perform this analysis may be very time-consuming for large data-sets, but
Software tools are available to perform this analysis (Laguna & Marklund, 2013).
Two commonly types of goodness-of βfit tests are the π2-test and the Kolmogorov-
Smirnov-test.
3.9.3 π2-test
The π2-test can be used to the the hypothesis that the data belong to a specific distribution.
The hypothesis is described by (Blom, et al., 2005):
π»0: π(π΄1) = π1, π(π΄2) = π2, β¦ . . , π(π΄π) = ππ(π), πππ πππ¦ π (πππ π‘ππππ’π‘πππ πππππππ‘ππ)
Blom et Al (2005) explain that a common procedure is to use the maximum-likelihood
method based on the observations to estimate the distribution parameters. T is then
calculated as:
π = β(π₯π β πππ
β)2
πππβ
π
π=1
(10)
π₯π = πππ‘π’ππ πππππ’ππππ¦ πππ π‘βπ πππ π’ππ‘
π = π‘ππ‘ππ πππ‘π πππππ‘π
ππβ = ππ(ππππ
β )
To be tested and compared to the tabulated value for π2 (r-k-1), where k is the number of
estimated parameters. The hypothesis π»0 can be rejected on the significance level Ξ± if
π > ππΌ2(π β π β 1). It is important to point out if π β€ ππΌ
2(π β π β 1) it does not mean that the
data follows the specific distribution, but rather that the hypothesis that the data follows the
distribution, cannot be rejected (Blom, et al., 2005).
21
3.9.4 Kolmogorov-Smirnov test
The test compares the empirical distribution function with the cumulative probability function
of the tested distribution. The empirical distribution function has the following form (Laguna &
Marklund, 2013):
πΉπ(π₯) =ππ’ππππ ππ π₯π < π₯
π(11)
Where π₯π,.., π₯π are the values of the sampled data. The test measures the largest deviation
between the theoretical and empirical cumulative probability distribution functions, for every
given value of x. Laguna and Marklund (2013) explains the procedure for the test.
1. Order the sampled data from the smallest to largest value
2. Compute D+ and D- using the theoretical cumulative distribution function οΏ½ΜοΏ½(π₯):
π·+ = max1β€πβ€π
[π
πβ οΏ½ΜοΏ½(π₯π)] (12)
π·β = max1β€πβ€π
[οΏ½ΜοΏ½(π₯π) βπ β 1
π] (13)
3. Calculate D=max (π·β, π·+).
4. Find the KS value for the specified level of significance and the sample size n.
5. If the critical KS value is greater than or equal to D, the hypothesis that the field data come
from the theoretical distribution cannot be rejected.
22
23
4 Empirical Context
This chapter describes relevant information about the company. The supply chain is
depicted, and relevant processes and activities are explained. The purpose of this chapter is
to build a foundation for the analysis, identifying current parameters and situations while also
introducing the reader to how the company currently operates.
4.1 Supply chain
The company uses a make-to-stock policy to provide goods to its customers. The companyβs
supply chain in Sweden is illustrated with the high level flow chart, provided in Figure 6
below. The colour coding explained in Figure 6 illustrate which department is responsible for
each operation.
Figure 6: The companyβs supply chain in Sweden
Starting from the suppliers at the left side of Figure 6, the raw material is received at the
processing facility. Packaging materials such as glass bottles and labels are received at the
warehouse facility. These raw materials are purchased from a multitude of suppliers, from
Sweden, Europe and other parts of the world. After the beverage is produced it is sent to be
tapped and packaged in an operation called packaging, in which there are several different
productions lines.
From the packaging department pallets are sent to the finished goods warehouse where the
majority of the stock is kept. Apart from this main warehouse at the production site, the
company also rent warehousing space and services from a third-party logistics service
provider, when the capacity of the main warehouse is insufficient. Most of sales need to be
shipped from the companyβs warehouse, and stock moved to external warehouses most
often need to be brought back to the main warehouse before being shipped. At the X-docs,
see Figure 6, goods are consolidated for transports to its end customers.
24
If SKUs are needed at a certain time when it cannot be produced because of limitations and
complexity in the production, SKUs and liquids can be sourced from other manufacturing
units.
4.2 Processing
This section presents the relevant aspects of the operations under the department
responsible for producing the beverage.
The beverage is produced using raw material delivered to the incoming warehouse and then
stored in pressurised bulk tanks. Various production constraints for various products should
be considered in this step. For some articles, extra constraints exist for the size of the batch
due to raw material packaging that must be consumed immediately after it is opened. In this
instance the batch size must correspond to a multiple of raw material packages. For other
articles, constraints exist for the size of the batch due to the tank sizes. There is a minimal
production volume affiliated with all products.
4.3 Packaging
The products are packaged at the packing lines in the manufacturing unit. The packaging
facility contains seven packaging lines which use several types of bottles and cans in
different volumes and with different production rates.
The packaging lines are open for production in accordance to the shift applied to that line,
see Table 1. The time that employees are present at the lines is called the lines βopening
hoursβ. This should not to be confused with the production hours of the line, which is the time
of actual production. Other activities that are done during the opening hours are cleaning,
training of personnel and maintenance. Table 1 shows the opening hours for each of the
shifts used.
Table 1: Opening hours in production during a week.
The first activity at the line is to fill a package with its product. After that the packages are
consolidated into larger selling units called pieces. The last activity at the line is to put the
pieces on a pallet. The activity with the lowest throughput, the βbottleneckβ of the machine, is
the actual filling of the package.
All products manufactured by the company is associated to a specific βrecipe groupβ. A
recipe group is a range of products, defined by the company that shares the same
characteristics. Each recipe group, and consequently all products included in it, can only be
packaged on one line.
Shifts Hours
1-shift 40
2-shift 76
3-shift 114
4-shift 138
5-shift 168
25
4.3.1 Production Fulfilment
The production fulfilment of the packaging lines states how much of the planned volume per
week that was produced. The planned amount is the amount set for production the Sunday
before the production week, which is measured against the actual output the Sunday at the
end of the week. This amount can vary greatly, and the resulting volume for a week can both
be higher and lower compared to the planned volume. Reasons for lower output than
planned include machine breakdowns, issues that result in a lower production speed or a
problem in material supply. Reasonings for a higher than planned output most notably
includes a higher production speed than planned for and consequently an increase from the
plan for lines starving for capacity. This puts extra strain on suppliers and purchasing
department to make sure there are material in stock in case of extra production.
As can be seen in Table 2 below, the mean of the production fulfilment is generally below
100%. A production fulfilment below 100% signifies a yield loss, while a production fulfilment
of above 100% signifies a yield gain. Later in the report both shall be named yield loss,
where a negative yield loss signifies a yield gain.
Table 2: Average production fulfillment during the last 4 years for the four studied production lines.
4.3.2 Changeover Process
The company use several production lines to produce their SKUs. Since the number of
production lines are considerably less than the number of SKUs, and the machine need to be
adjusted for different kind of SKUs, all lines are subject to changeovers.
The changeover requires different operations depending on which combination of SKUs is in
succession of each other, signifying that the time for changeover is sequence dependent. For
example, a change from a 12-pack to a 6-pack of the same beverage is fast while a change
from a fruity beverage to a clear carbonated water will require additional operations.
The characteristics of the changeover, and the times and costs associated with it, vary from
line and type of product. For weeks close to current time, where the production sequencing is
known, a matrix is used to determine the planned changeover time in the production. For
long-term planning, the sequencing is not known, and estimation must be used.
Two different definitions of the changeover time in the production exist in the company. The
packaging operations define the changeover as tap-to-tap. This means the time from where
the last package was filled of the old batch to the time where the first package is filled from
the new batch. The planning department on the other hand define the changeover time as
what is referred to as pallet-to-pallet. This is the time from where the last full pallet was
26
retrieved of the old batch by the forklifts to the time where the first full pallet of the new batch
is retrieved.
The taping is the bottleneck on all lines in the packaging department.
Each changeover carries a cost of cleaning materials and a start-up waste in beverage. The
time spent on changeover is also costing the company employee-time not spent producing.
The lines are subject to fixed costs of depreciation, maintenance, utilities etc. The time spent
doing changeover also result in more volume that need to be sourced, inducing more costs.
Since determining these costs have not been a goal of the thesis, and the gathering of this
data have been deemed to extensive for this project, these costs will be taken at face-value
from the production controllers of the company.
Three different suggestions to approximate the changeover cost have been considered. First,
all changeovers taking place on a line could be said to carry the same cost. Secondly,
approximating on a recipe group level results in that only similar products carrying the same
changeover cost. Lastly, an estimation on a SKU level could be done, resulting in all SKUs
having their individual changeover cost. The chosen approach for this thesis is the recipe
group level and the reasoning for this will be explained in chapter 5.
After the packaging operation is done and the pallets of produced SKUs are finished they are
picked up by LGVs (Laser Guided Vehicles) and transported to the warehouse.
4.3.3 Line Efficiency
One of the major KPIs the packaging department is measured on is their output compared to
the maximul theoretical output of the machines. One-hundred percent efficiency is defined as
the line running full speed all the available time (opening hours), i.e., the entire time
operators are scheduled to work. The efficiency is then the ratio of actual time run with the
actual speed and the available time there are operators available running on maximum
speed.
In a perfect world the difference from the actual efficiency and the maximum efficiency would
be due only to change-over downtimes. However, the lines do not always run on maximum
capacity when online, and they are subject to breakdowns and other stops reducing
efficiency further.
Figure 7 below shows an example of how the opening hours is allocated on one of the lines.
OEE (Overall Equipment Effectiveness) is the fraction of time the machine is running on full
speed.
27
Figure 7: Activity distribution for the open time of line X.
The relationship between changeover time and efficiency is clear, the efficiency loss is
simply the changeover time divided by the total time. The relationship between breakdown
and efficiency is also clear, breakdown results in an efficiency of zero for the disrupted time.
The deviation from maximum line speed when it is running can be explained by several
different factors. These include different mechanical problems, retrieval problems in the
warehouse and ramp-up issues.
4.4 Warehouse
The company uses several warehouse facilities. Beside the main warehouse, the company
have throughout 2017 rented spaces in four external warehouses. The inventories are
transported between the locations by an external truck company. When the company ship
inventory between the warehouses, they have the option to purchase a transport with goods
one way (single transportation) or transportation of goods back and forth to a warehouse
(double transportation). There is no special dedication of the articles to specific locations in
the warehouses.
It is the planning department that decides what to transport between the warehouses and
when. The decision is then communicated to the warehouse department which handles the
administrative process of booking transportations and preparation of goods to be
transported. The planning department receive a suggestion from SAP of what goods that
should be transported and when, although what the planner chose to ship often deviate from
SAPβs suggestion.
How the finished goods are distributed among the warehouse is presented in figure 8 below.
44%
36%
7%
5%4%
2%
Line X OEE
Breakdowns & defects
Change over includingrelated cleaningCIP and cleaning
External Stops & Losses
B&D speed looses
Organisational Losses
Maintenance activities
Start Up/Shut Down
28
Figure 8 stock on hand at the warehouses dated back to January 1, 2017.
Figure 8 illustrate that the external warehouses are always used. The number of stored
pallets at the external warehouses are varying throughout of the year while the main
warehouse inventory are kept at around 27 000 pallets which corresponds to a utilization of
75%. This utilization is expressed as a target utilization in the main warehouse. The
variations of inventory levels are an effect of seasonality and variations in demand which will
be more thoroughly explained in the analysis.
4.5 Information systems
The company utilize several different IT systems to align and streamline daily operations and
strategic decisions. This chapter will provide a brief overview of these systems.
4.5.1 SAP
SAP is the ERP (enterprise resource planning) system used by the company. It integrates
and consolidates information form the whole enterprise, serving as the working platform for
several functions of the company. This report will mainly focus on SAP functions tied to the
planning of production and warehousing operations.
4.5.2 Production follow-up tool
As a graphical feedback tool from the production, the company uses a self-developed
software. From this application the user can quickly and easily get a good grasp of how the
production is performing. The information in the follow-up tool is available for all departments.
4.5.3 MES
The companyβs manufacturing execution system (MES), serves as the interface between the
rest of the information architecture and the production floor. The MES measures, controls
29
and serves as the interactive software for the operators to enter or retrieve information to
SAP.
The MES collect real-time data and transfer it both to the production follow-up tool and SAP,
allowing the planning department to act in time to avoid or lessen the consequence of
complications.
4.5.4 Warehouse Management System (WMS)
While SAP keep track of the high-level inventory management, the WMS have low level,
more exact, information of the flow in the warehouse. As an example, SAP only have
information of which SKUs that are kept in a warehouse and in which quantities, while the
WMS can point to the exact location in the warehouse. The WMS is also used for planning
and keeping track of ingoing and outgoing shipments
4.5.5 Business Intelligence software (BI)
The company uses a business intelligence service to retrieve data from SAP in manageable
report formats which can also be converted to excel format. The service is flexible, and users
have the ability to create new reports by using preset templates which can then be shared
with other employees, creating a standardized report format which can be used for analysis.
As all the systems are connected to SAP, and the BI retrieves and presents the data from
SAP, the BI can present data originating from the MES or WMS. This gives full insight in
these systems from the BI.
4.6 Inventory Control
This section presents the relevant aspect of how the company is controlling their inventory
and how their results are measured.
4.6.1 Batch Size
Currently the company does not use any theoretical model to determine the batch size in their production. SAP uses a batch quantity when scheduling the production that is based on either a fix quantity or the demand of a set number of weeks. These amounts are set when the product is accepted in the portfolio based on similar products and is iteratively updated if major failures are recognized.
4.6.2 Service Level
When a new customer order is received, the stock is immediately checked to verify that the
full volume of the order can be satisfied from stock on the specified shipping date. The
volume that is accepted is classified as ATP (Available to promise) and is confirmed to the
customer. The fraction of the volume that cannot be satisfied from stock is classified as PO2-
volume and is rejected. HL is an abbreviation for hectolitres.
ππ2 β π£πππ’ππ = πΆπ’π π‘ππππ πππππ (π»πΏ) β π΄π£πππππππ π‘π ππππππ π(π»πΏ)
30
When the promised order is to be picked from stock there is a chance that this picking will
fail. Causes for this failure can include for example a stock-balance error or unforeseen
errors in the production between the order confirmation and the shipping date. Volume that
can be picked are classified as PA (Product availability) and volume that cannot be picked
are classified as PO4-volume.
ππ4 β π£πππ’ππ = π΄π£πππππππ π‘π ππππππ π(π»πΏ) β π΄π£πππππππ ππ‘ πππππππ(π»πΏ)
The company differentiate the required service level between their products, based on the
products strategic importance for the company. The departments are measured on what they
call βstock service levelβ, which is the part of the total ordered volume that can be satisfied
from stock. Linking to chapter 3.5 this is the same definition as for S2 in the literature.
Formally, the stock service level is defined as:
πππΏ = 1 β (β ππ2 + β ππ4 π£πππ’πππ
β πππππ π£πππ’ππ) (14)
4.6.3 Safety stock
The company base their safety stock calculation on a formula commonly used in industry.
(King, 2011)
ππ = π β β(πΏπ β ππ·2) + (ππΏπ β π·π΄ππΊ)2 (15)
Where:
π = π β π ππππ ππ π ππππ‘π¦ ππππ‘ππ (π ππ‘ ππ¦ ππππ’ππππ π πππ£ππππππ£ππ)
πΏπ = πΏππππ‘πππ in weeks
ππ· = ππ‘ππππππ πππ£πππ‘πππ ππ ππππππ per week
ππΏπ = ππ‘ππππππ πππ£πππ‘πππ ππ πππππ‘πππ per week
π·π΄ππΊ = ππ£πππππ ππππππ per week
This formula is derived from the cycle service level, or S1. (See chapter 3.5.2)
The company have made some alterations to the expression to customize it for their own
organization.
ππ = π β β(πΏπ β ππΉπΈ2 ) + (ππΈ. πΆπ) β π2 (16)
π = πππ€ π ππππ‘π¦ ππππ‘ππ
πΏπ = πΏππππ‘πππ in weeks
ππΉπΈ = ππ‘ππππππ πππ£πππ‘πππ ππ πππππππ π‘ πππππ per week
ππΈ. πΆπ = ππ’ππππ¦ π£πππππππππ‘π¦ per week
π = π΄π£πππππ πππ‘πβ π ππ§π
Exactly how this alteration was made is unclear and will not be researched further in this
thesis. The most important observation is that the average demand is no longer used but
31
instead the average historical batch size, a fact that need to be considered when examining
the consequences of altering the batch sizes.
4.7 Activities in the Planning Department
This section aims to present the activities and processes which take place in the planning
department. The section starts with introducing the operative aspects of how a batch size is
determined and continues with more tactical aspects of the departments work.
4.7.1 Operative planning process
The planning department is planning what to produce at the different filling-lines and when to
produce it. To do so, also the availability of raw material and the beverage needs to be
considered. The production plan is shared with the filling line, the processing department and
the warehouse to enable coordination of their operations. The procedure followed by the
planning department is presented in Figure 9 below where the figures in the vertical line
represent activities related to determination of the batch sizes. The figures to the left of the
vertical line relate to activities in other parts of the supply chain. The work is facilitated by the
SAP modules APO and ERP.
Figure 9 The operative planning process
SAP looks at the forecasted demand and inventory levels for the SKUs to suggest a
production plan where production orders of all SKUs are put in. The order quantity is
determined by choosing between a fix order size for the SKU and a dynamic order size equal
32
to a number of weeks estimated demand. The program does not take into account any form
of capacity constraints.
The activity called Capacity levelling are performed in SAP every Sunday. In this activity SAP
adjust the batch sizes by taking input from available capacity on the production e.g. shifts for
the line and comes up with a suggested production order.
From the created production order SAP suggests purchase quantities for raw material for the
external supply planning, and beverage requirements to the processing, in Figure 9 called
MRP 1&2.
After these activities, the manual planning starts. Planners can change the batch sizes and
the production order to increase the efficiency of the filling line and simplify the handling of
the goods in the finish goods warehouse.
In the activity called confirmation a planner confirms the order which makes it possible to see
it in the companyβs internal production system follow-up tool. In the activity called job
releasement the status of an order changes from confirmed to released which means that the
order is ready to be produced.
4.7.2 Stock building
The company have stated that during most the year one or more lines are in a stock building
period i.e. in a period where they are pushing the inventory levels up in anticipation of a
period where demand exceeds capacity. This need is displayed in Figure 10, which show the
demand for each week divided by the maximum demand during the year and the maximum
capacity of the line. The week with the highest demand of the year is, naturally, the week
with the value 100% on the y-axis.
Figure 10: Demand of SKUs produced by line Y throughout the year, and the capacity of the line.
As is evident by the figure, the demand greatly surpasses the capacity of the line some
periods of the year, and thus the stock need to be built up in anticipation of this during the
weeks of lower demand.
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
Demand distribution
Demand Capacity
33
The company is currently handling this situation by producing ahead of demand, and when
this is not enough the products are sourced from elsewhere in the world. This results in
higher cost of breakdown and changeover for these lines as any lost production volume will
need to be procured from other alternatives. All non-productive time can be translated to lost
produced volume and therefore more sourced volume. The sourced volume carries a high
cost and thus the profit margin is significantly reduced.
4.7.3 Cycle planning of SKUs
Each SKU in the companyβs portfolio can only be produced on one line in the production
facility. Since the difference of the product before and after the changeover is the major
influence on how long time the changeover will consume, there is a strong incentive to run
similar products in sequence. The company have translated this insight into cycled schedules
for their production. For example, one week the line only produces fruity beverage and other
week, only non-fruity beverages. This example entails that the cycle is two weeks for these
products since every production would need to satisfy demand for at least two weeks until
the next production. A common procedure is to include articles from the same recipe-group
in the same cycled schedule.
4.7.4 Sales and Operations Planning at the Company
Sales and operations planning is a business process which is used by the company, and a
structured procedure is followed. The procedure has four steps which are performed every
month: Demand Review, Supply Review, Demand & Supply Reconciliation and Monthly
S&OP meeting. The S&OP process which is performed in each country separately, is
outlined in Figure 11. The arrows present the responsible function for the activity while the
bullet points are the output from the activity.
34
Figure 11: The S&OP process at the company.
The process starts in the sales function where the marketing strategy, planned marketing
initiatives and the forecast are analysed to derive the demand plan. The risks and
opportunities of this plan are highlighted.
In the second step, the supply chain reviews their capabilities to facilitate this plan and
update the plan according to their constraints. The review includes analysing the available
capacity and if sourcing is necessary. Also, the risk and opportunities from the supply chainβs
perspective are highlighted. In times of uncertainty, the company need to make sure that it
has a certain amount of buffer capacity i.e. a certain time where nothing is planned, to be
able incorporate necessary additions to the plan.
In the step Demand and Supply Reconciliation, the demand and supply are aligned between
managers from the sales department and the managers in the supply chain. The action plan
is also updated together with the risks and opportunities.
In the fourth step each countryβs management team signs off on the plan. In each step the
meeting time is tracked to evaluate the efficiency of the meeting.
35
In this way, the company is using their S&OP process with a bottom-up approach. The
information is gathered in the departments and shared to be aligned in the company with
guidance from senior management. The company use four KPIs related to the S&OP
process namely Stock Service Level (SSL), Forecast Accuracy (FA), Forecast Bias (BIAS),
Obsoletes as % of Cost of Sales (% CoS).
36
37
5 Analysis
This chapter present how the theory is used to create the quantitative model to represent the
companyβs situation. The intention is also to examine the consequences of different
proposals to solve the problem, as well as other problems found during the analysis.
Throughout the chapter we will refer to the model to when results are presented. A closer
outline of the model will be presented in the next chapter.
5.1 Mathematical Lot sizing
The purpose of the report was partially set to, create a quantitative model that takes relevant
costs and variables into account when determining the production batch sizes. The model
should be an asset to the planning team that can relatively easily be incorporated in the
planning operations. The model should not be too vulnerable to variations in the performance
of the supply chain and must be able to support many SKUs and production lines. It should
also be easy to maintain and uphold while being relatively easy to understand. Three ways of
modelling the lot sizing problem was presented in chapter 3, and in this section one of these
will be chosen for this thesis.
5.1.1 EOQ
The EOQ formula suffers from drawbacks and assumptions, including:
1. Demand is constant, continuous and deterministic.
2. Ordering and holding costs are constant over time.
3. The whole batch quantity is produced instantaneously and delivered at the same
time.
4. No shortages are allowed.
The question is not if the EOQ-formula is a perfect representation of reality but rather if it is
βgood enoughβ for the companyβs operations. A case shall be made for each point.
The first point, where the demand is assumed to be constant and continuous is likely the one
that will be the hardest to justify. The demand of beverages varies widely for different
seasons, for example, some beverages has a significantly higher demand during summers
and some sodas only sell during winter. This weakness can, in general, be mitigated by
increasing the frequency of the EOQ-calculation, especially for products that vary heavily.
As for the demand being deterministic, the consequences of this assumption will be
discussed further when calculating the safety stock
The second assumptions, that ordering and holding cost are constant over time, hold true
during the period between calculations, at least at a SKU level.
The third assumption instantaneous production and delivery is not consistent with reality.
However, the production time is generally negligible compared to the holding time of the
batch. A run that last for 5 hours and satisfies demand for one week can in the opinion of the
writers be assumed to be instantaneous.
38
As the fourth point states, no shortages are incorporated since incoming customer orders are
rejected if there is no stock on hand.
Finally, from chapter 3 it is also known that the EOQ-formula is not very sensitive to either
having the wrong cost parameters, since for example a miscalculation in the order cost by
50% only affect the cost by 2%. The theory also suggests that straying from the calculated
order quantity by a small amount does not have major impacts on the cost either, a fact that
fits well with the companyβs operations where there are other factors to consider than the
total cost.
Even though the EOQ-costs is only a modelled representation of the companyβs cost this fact
is still seen as an implication that the model is robust.
5.1.2 Wagner-Whitin
The Wagner-Whitin largely follows the same assumptions as the EOQ, with the exception
that the demand is no longer considered to be constant. The Wagner-Whitin have been
found to be problematic to use in the companyβs MRP-system setup since there is no
obvious way to choose the value of T, the number of periods calculated. There is also a
problem that the demand is far from deterministic, faltering the whole point of the Wagner-
Whitin optimization.
A considerable problem that have identified with the Wagner-Whitin algorithm is the difficulty
of incorporating it in a model that handles the large number of SKUs that the company have
in its portfolio.
5.1.3 Silver Meal
While the silver-meal heuristic is easier to compute, it suffers from the same limitations as
the Wagner-Whitin, namely the difficulty to produce an excel-model computing the optimal
batch size for a large number of SKUs easily at the same time.
5.1.4 Chosen Model
This master thesis will proceed with the EOQ-model, largely because of the reasons just
stated. The EOQ-model presents a solution to the problem with the lot-sizing with the
characteristics requested earlier, namely:
β’ Easily implemented in the workflow.
β’ Relatively easy to maintain.
β’ Easily scalable to many SKUs in an excel model.
The rest of the analysis will be conducted with the chosen mathematical model in mind. The
batch size given from the EOQ-formula is denoted Q*.
39
5.2 Changeover Cost
This section presents analysis related to the changeover cost and how it is derived for the
company.
5.2.1 Changeover Times
In chapter four (empirical context) two separate times for changeover were defined and three
different hierarchical levels to average the changeover times were suggested. It is now time
to make a case for which of these will be used in the model.
As discussed in chapter 4, different departments at the company use different definitions of
what the changeover time includes. Since all production lines share the fact that the bottling
station is the line bottleneck it has been decided that the βtap-to-tapβ time is the proper
definition to use in this thesis. The reasoning for this is that it is when the tap is idle that the
production is losing production time.
Moving on, we remind the reader that three different levels to measure the changeover time
have been identified. Either an average for the line, for the recipe group or for the individual
SKU can be used. The level used should accurately represent the impact a product has on
the changeover cost over time. Starting with the approach to average on a SKU-level, this is
problematic since some SKUs are systematically placed at the beginning of a chain of
products from the same recipe. Consequently, this SKU will be punished by always having a
longer changeover time than the rest of the SKUs from the same recipe, which will βfreeloadβ
on this.
Concerning the other two levels, line or recipe group, an analysis of how consistent the
changeover time is on each level have been conducted. If all the recipes on a line would
show similar changeover times it would be fair to say that the line itself have one change
over time associated with it. If on the other hand the recipes vary this would not be a good
approach since recipe groups with a longer and more complicated changeover would cost as
much as easier change overs. Table 3 below show the different average changeover times of
recipes at line I. Each cell represents one recipe group used on the line. The samples of
changeover times are used to illustrate the variability.
Table 3: Average change over times of different recipe groups on one line during 2017 in minutes.
From Table 3, it can be concluded that the changeover times on a line vary heavily from
recipe to recipe.
In turn, table 4 illustrate that the different changeover times for each SKUs in one of the
recipe groups, are relatively similar.
81,5 63,9 59,3 68,8
93,9 32,2 59,4 244,0
99,3 147,7 52,7 49,3
86,5 66,2 129,3 53,4
121,6
40
Table 4: Average changeover times of different SKUs in a recipe group during 2017 in minutes.
Generally, the changeover times are more concentrated in Table 4, except for one entry that
suffer from the problem described in the previous section. The conclusion of this analysis is
that the most appropriate level to average the changeover times for are on a recipe group
level.
The actual modelling for the average time is simple, consider the scenario that for a set
period of time, t, x number of changeovers have been conducted. During the time t, y amount
of time was spent performing the changeovers. Using simple arithmetic, one can arrive at the
conclusion that the average changeover time equals the total time spent divided by the
number of occasions, π¦
π₯.
5.2.2 Fixed changeover cost
Each changeover carries a fixed cost due a combination of material used and a fix ramp up
time for the next production. The material includes cleaning supplies and wasted beverage
due to start up and the time is tied to the ramp-up of the line when restarting production. The
ramp-up time is not included in the actual changeover but can be seen as an efficiency loss
for the next production. The ramp-up time is as stated before fix, but it carries hourly variable
costs discussed below.
5.2.3 Variable Changeover Cost
The variable changeover cost is tied to the employee cost and the cost of lost production.
Since the company uses a make to stock system, only a line in the need of sourcing to
satisfy the demand carries a cost of lost production. This cost is the cost to source the
quantity βlostβ due to the stop in production. The employee cost is different depending on the
shift but is essentially just cost per hour for the line.
5.2.4 Total changeover cost
The cost per changeover is the cost associated with changing from an arbitrary SKU to the
SKU in question. This cost is simply the product of the changeover time and the changeover
cost per hour as derived in the two previous chapters.
ππΆπΆππΎπ = πΆπ + (πΆπ£ β π‘π) (17)
ππΆπΆ = πππ‘ππ πΆβππππππ£ππ πΆππ π‘ πππ ππΎπ
πΆπ£ = ππππππππ πππ π‘ πππ βππ’π (πΏπππ π πππππππ)
π‘π = ππππ πππ πβππππππ£ππ (π πππππππππ’π π πππππππ)
πΆπ = πΉππ₯ππ πππ π‘
41
The actual costs have been given from the controllers in the production.
5.2.5 Outcome
The results for the changeover costs are illustrated in Table 5. The costs can be applied as
the changeover cost (A) in the EOQ formula, for the SKUs in the recipe-group.
Using the approach presented above, the changeover costs vary greatly between recipe
groups belonging to the same production lines. In Table 5 the changeover costs at the four
lines included in the study are presented.
Table 5: The Changeover cost for all recipes in SEK. Each cell in the columns represent one of the recipes of the line.
The underlying reason for these variations are differences in the measured average
changeover times historically for the different recipe groups. The reason that these times are
so different is not something that will be investigated further in this report but will be left for
future research.
5.3 Holding cost
This section will address how a suitable holding cost for the companyβs supply chain were
obtained. The approach follows the ABC-method for determining the holding cost. Necessary
assumptions to determine the holding cost are explained throughout this section. The unit
used in the EOQ-formula is hectolitre (HL).
Two different holding costs have been determined based on the activities in the warehouses.
The first holding cost is for the external warehouses (βπΈππ). The second holding cost is for
Line X Line Y Line Z Line I
6133 15081 17393 13983
7300 18200 18687 14631
7399 18291 19578 14853
7733 18672 20305 15224
7950 19134 22153 15578
8191 19509 23326 16609
8454 20367 23801 19915
8512 20506 25286
8578 20793 34707
8807 22622 56238
8996 23033
9005 24090
9883 24869
10287 28054
10392 29161
10493 34228
11719 45568
12174
12386
13406
14101
14305
14420
42
the main warehouse (βπΉπ΅πΊ). βπΈππ is used to determine the batch sizes in today's operations,
and βπΉπ΅πΊ are used to determine potential future batch sizes with an extension of the main
warehouse. To obtain the cost of holding a pallet per day, last yearβs costs have been divided
with the average number of stored pallets. The procedure of calculating βπΉπ΅πΊ and βπΈππ is
more closely described in the next sections.
The later described procedures capture the costs of the activities in the warehouses. Added
to the activity costs are also the cost of capital tied up in inventory. The cost of capital tied in
inventory originates from the expected yearly return of investment which is set by the
financial department of the international group. The cost of capital tied up inventory is
calculated as:
ππΆπ =πΆππΊπ β πΈπ ππΌ β πππΎπ
π€ππππ πππ π¦πππ(18)
πΈπ ππΌ β πΈπ₯ππππ‘ππ π¦πππππ¦ πππ‘π’ππ ππ πππ£ππ π‘ππππ‘ [%]
πΆππΊπ β πΆππ π‘ ππ πΊππππ ππππ [πΆππ π‘ πππ π»πΏ]
πππΎπ β ππππππ‘ ππππ’ππ [π»πππ‘ππππ‘πππ πππ ππππππ‘]
In this way a cost per pallet and week associated to capital tied up in inventory is obtained.
This cost is unique for each SKU since each SKU has its own production cost.
5.3.1 Holding cost in todayβs operations
To represent the out of pocket holding cost per pallet and week in todayβs operations, only
βπΈππ is applied in the model, for all SKUs. The motivation is that there is no special
dedication of positions in the warehouses for the SKUs. Which essentially means that even if
a pallet is stored in the main warehouse, it pushes another pallet to the costlier external
warehouses. Throughout a year, pallets are always stored at the external warehouses, which
justifies the approach.
The companyβs payments related to the external warehouses are associated with
transportations, rent and handling. The costs in the companyβs system are structured under
these categories. Last yearβs costs, scaled down to the cost per day, are used to determine
βπΈππ:
βπΈππ = (β π π
ππ=1
ππΈππ+ ππΆπ) β
1
πππΎπ
(19)
π π β π·ππππ¦ πΆππ π‘ πππ πΆππ‘πππππ¦ π
ππΈππ = π΄π£πππππ ππππππ‘π ππ πππ πππ¦ ππ πΈπ₯π‘πππππ ππππβππ’π ππ
π β ππ’ππππ ππ πππ‘πππππππ
The procedure is enabled by assuming that the costs, and number of stored pallets at the
external warehouses, will be approximately the same under next year as the last year.
43
5.3.2 Holding cost for an extended internal warehouse
It is assumed that by extending the main warehouse no external warehouses would be
required. Therefore only βπΉπ΅πΊ are used in the model to represent this situation. Another
assumption is that the holding cost for a pallet will be the same in an extended internal
warehouse, as the holding cost per pallet in the internal warehouse today.
The categories associated with handling a pallet in the main warehouse are rent, personnel,
equipment and maintenance. The yearly costs are scaled down to daily costs to determine
βπΉπ΅πΊ with Equation 20.
βπΉπ΅πΊ = (β π π β ππ
ππ=1
ππΉπ΅πΊ+ ππΆπ) β
1
πππΎπ
(20)
π π β π·ππππ¦ πΆππ π‘ πππ πΆππ‘πππππ¦ π
ππ β ππππππππ πΉππππ‘πππ πππ πΆππ‘πππππ¦ π
ππΉπ΅πΊ = π΄π£πππππ ππππππ‘π ππ πππ πππ¦ ππ πΉπππππππππ
π β ππ’ππππ ππ πππ‘πππππππ
The marginal fractions are assumed by the authors of this report while the costs are numbers
from last year. This is done with the help of the supply chain director and his team, providing
us with reasonable numbers.
The reason different categories are used in the procedures, is that the costs originate from
different sources. βπΉπ΅πΊ originates from internal costs in the company and βπΈππ originates
from actual payments to the third-party logistics company. The cost in both procedures are
obtained from the warehouse controller. Although different categories are used, both
procedures are capturing the cost of space and the handling.
5.4 Demand
The demand is modelled as a weekly average based on the forecast for the upcoming six
months. In the model, the demand on SKU-level is used since it is chosen to be most
representative because variations of demand among the recipe groups and the lines exist.
The reason six months is used is because the model is primarily going to be updated after
this time, in connection with the update of the safety stock. Figure 13 describes the
aggregated demand on the four analyzed lines in the study throughout the year.
44
Figure 12. Demand for the SKUs on the four lines throughout the year.
Figure 13 indicates that seasonality exists among the articles, but not necessarily for all
articles. Typical time periods with high demand is the summer, Christmas and Easter. The
approach of using the average weekly demand over six months does not capture the
seasonality and can be problematic to use for all articles since the demand is an input to the
EOQ-formula. This is a shortcoming in the used approach further discussed in chapter 7.
5.5 Constraints in Processing
This section presents a procedure to include processing-constraints in the model. The
constraints accounted for in this project is the quantified minimum batch sizes and the size of
the raw material units. As stated in chapter four (empirical context). Certain SKUs are
produced from raw material with short expiry date. Therefore, the whole raw material unit, or
multiples of units, must be used to produce the batch. The minimum batch sizes and
multiples therefor delimits the batch sizes which can be used. The used procedure is to
adjust Q* to the closest multiple or to the minimum batch size. Table 6 below show Q*, the
minimum batch sizes, the sizes of multiples and the constrained batch sizes for a selection of
SKUs. The unit in the table is hector liter. The selection of SKUs is based on SKUs with
representative constraints. The unit of the batch sizes in Table 6 is hectoliter (HL).
Table 6: Consequence of constraints on batch size
0%
20%
40%
60%
80%
100%
120%
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
Demand
45
5.6 Statistical analysis related to Perished Goods
This section presents how the demand, forecast and the forecast error are analysed to
evaluate how a maximum batch size could be determined based on statistical data for the
parameters. The unit of measure in the analysis is Hectolitre (HL). The maximum batch size
is determined based on the acceptable risk for perished goods. The volume corresponding to
the acceptable risk is calculated with the cumulative distribution function based on the
stochastic demand during the SKUβs sellable time. The expected volume of perished goods
associated with a batch is thereafter calculated. The approach presented in this section is a
complement to the EOQ-calculations.
5.6.1 Maximum Batch Size
This section presents how the maximum batch size is determined. The chosen approach is
based around an acceptable risk of perished goods. The analysis of the statistical
parameters is carried out on a monthly basis such that every month become a sample. The
sample size is chosen to a maximum of 38 months but varies between the SKUs depending
on available data. The forecast error (FE) is defined as:
πΉπΈ =πΉππππππ π‘ππ πππππ β π΄ππ‘π’ππ πππππ
πΉππππππ π‘ππ πππππ
To determine if it is suitable to model FE with a normal distribution the data was examined.
Figure 17 shows the histogram for an article which indicate that a normal distribution might
be suitable for this particular article.
Figure 13 Histogram of FE for a SKU.
The Kolmogorov-Smirnov test was used to test if FE could be approximated to be normally
distributed with the mean and standard deviation of FE from the samples. The Kolmogorov-
Smirnov test for this article gave that the null hypothesis (H0) i.e. the assumption that FE is
normally distributed, could not be rejected on the significance level 0,05. The conclusion for
this article was that it could be modelled as a normal distribution as:
πΉπΈ β π(ππΉπΈ , ππΉπΈ)
ππΉπΈ = 0,01
ππΉπΈ = 0,14
0
2
4
6
8
10
12
-0.5
-0.4
5
-0.4
-0.3
5
-0.3
-0.2
5
-0.2
-0.1
5
-0.1
-0.0
5 0
0.0
5
0.1
0.1
5
0.2
0.2
5
0.3
0.3
5
0.4
0.4
5
0.5
Frequency
46
The Kolmogorov-Smirnov test was performed on 230 SKUs, individually. The results were
that for 204 of the 230 SKUs that were studied, H0 could not be rejected on the significance
level 0,05. The model also includes SKUs where no data were available to perform the
Kolmogorov-Smirnov test. A discussion of how rejected null-hypothesis and SKUs without
data were handled are presented in section 5.6.3.
Every SKU has an expiration date when it no longer can be sold to the customers. The dates
vary from one to 22 months. The forecast error is used to describe the expected demand and
how the demand vary during the time a batch could be sold. The demand during this time is
modelled as a normally distributed stochastic variable (Y) with the following parameters:
ππ·πππ = π β ππππ‘βππ¦ πππππππ π‘ππ ππππππ
ππ·πππ = βπ β ππΉπΈ β ππππ‘βππ¦ πππππππ π‘ππ ππππππ
π β π(ππ·πππ , ππ·πππ)
The parameters are defined as:
ππ·πππΏ = πΈπ₯ππππ‘ππ ππππππ πππ π ππΎπ ππ’ππππ π‘βπ π‘πππ π πππ‘πβ πππ ππ π πππ π‘π ππ’π π‘πππππ
ππ·πππΏ = ππ‘ππππππ πππ£πππ‘πππ ππ ππππππ πππ π ππΎπ ππ’ππππ π‘βπ π‘πππ π πππ‘πβ πππ ππ π πππ.
π = ππ’ππππ ππ ππππ‘βπ π πππ‘πβ πππ ππ π πππ π‘π ππ’π π‘πππππ
The procedure is based on the theory of linear combinations (see section 3.9.1) and the
assumption that the monthly demand is independent. More precisely, it is the stochastic
variable for one monthly FE that should be independent from the stochastic variable of
another monthly FE, for the approach to hold.
Goods perish when the batch size is larger than the demand during the time a batch can be
sold. The procedure enables us to derive a maximum batch size based on the acceptable
risk that perishable goods will occur, illustrated in Figure 14. This acceptable risk is therefore
what decides how large the batch should be under the given data.
Figure 14 illustration of risk for perished goods.
If the batch size exceeds this maximum batch size, the risk of perishable goods is greater
than the chosen risk level.
Pi
Demand (i)
Risk of Perishable goods
Specific Risk
Probability massfunction
47
The standard deviation of the forecast error (ππΉπΈ) indicate how difficult
the SKUs are to forecast correctly. The greater ππΉπΈ, the more the forecast errors vary. In the
analysis, no outliers were excluded which might have affected the results. The SKU in the
example above is a popular article with an overall accurate forecast but the model also
includes more troublesome SKUs with greater ππΉπΈ. Other possible reasons for a high
standard deviation is a small sample size, where the outliers have greater effect than in a
large one. Large ππΉπΈ are troublesome because they might give a distribution π β
π(ππ·πππΏ , ππ·πππΏ) with probabilities among negative demand which do not represent to the
reality. This is further discussed in section 5.6.3.
5.6.2 Expected volume of perished goods
This section builds upon the previous and explain how the expected volume of perished
goods are calculated. The stochastic variable Y and the maximum batch size can be used to
calculate the expected volume of perished goods for a batch, explained by (23).
πΈπ₯ππππ‘ππ π£πππ’ππ πππππ βππ πππππ = β ππ β (π β π)
π
π=0
(21)
ππ β ππππππππππ‘π¦ π‘βππ‘ π‘βπ ππππππ ππ’ππππ π‘βπ π‘πππ π πππ‘πβ πππ ππ π πππ ππ πππ’ππ π‘π π
π β π΅ππ‘πβ πππ§π
Table 7 present the volume of expected perishable goods (HL) for a selection of articles that
are chosen to be illustrative.
Table 7 results of MAXQ and expected perishable goods for a selection of SKUs.
In the analysis, the volume of expected perishable goods is obtained based on Q* from the
EOQ-Calculations. For the SKUs in the table the expected volume of perished goods varies
from 40 HL per batch and 0 HL per batch. The fourth column in the table indicate if Q* is
greater than the maximum batch size based on the chosen acceptable risk level. The
maximum batch sizes are presented in column 2 and Q* is presented 3. As expected, the
largest volumes of expected perished goods occur when πβ > ππ΄ππ.
48
5.6.3 Discussion of approaches
The calculated batch sizes provide a support to the theoretically determined batch size
calculated from the EOQ-model. In derivation of the maximum batch sizes, the risk for
perished goods is set to 5%. This percentage is empirically chosen and is suggested to be
set by the user based on what the company think is reasonable.
The maximum batch sizes and expected volume of perished goods are calculated with both
hext and hFBG applied in the EOQ-formula. Intuitively the expected volume of perishable goods
increases with an increased batch size as a result of a lower holding cost for the extended
warehouse option.
The problems of large ππΉπΈ, rejected H0 and articles without forecast data are handled by
assuming a normal distribution of FE with ππΉπΈ = 0,5, for the articles which suffer from any of
these drawbacks. The assumption of 0,5 is empirically chosen and guided by the other
standard deviations of the studied SKUs. To replace large ππΉπΈ with a lower value could be
seen as a standardized procedure to remove outliers. If ππΉπΈ > 0,5, it is replaced with ππΉπΈ =
0,5. The motive for the chosen procedure is the vast number of SKUs and that qualitative
input to remove outliers would be required for each SKU with a large ππΉπΈ, which not was
feasible within the time frame of this thesis project. The consequence of the chosen
approach is that it replaces high ππΉπΈ with a lower value which essentially is the outcome
when outliers are removed.
The assumption that the articles not included in the distribution fitting are normally distributed
are supported by the fact that the majority of the tested articles H0 could not be rejected. It is
therefore assumed that H0 cannot be rejected for the majority of the not tested articles,
although it cannot be confirmed beforehand.
Rejected null-hypothesis are indicated with the value NO in the sixth column in Table 7. In
this way the approach warns for when the values could not be trusted, due to the normal
distribution being a faulty choice.
Regarding the risk for distributions with probabilities at negative demands because of large
ππΉπΈ, the maximum of cumulative percentages for the distributions of the SKUs are calculated
to 0,56%. This percentage include articles with substituted ππΉπΈ. This low percentage is
considered to be of little impact for the results.
The presented approach uses an accepted risk for perished goods as a criterion to
determine the maximum batch size and the expected volume of perished goods. Another
approach would be to use the expected cost or volume of perished goods as a criterion to
determine the maximum batch sizes. These criterions can be seen as more relevant to base
the decisions on. Such a procedure was determined to be more complex and therefore not
chosen.
5.7 Resulting batch sizes from the model
The previously described approaches to determine demand, holding cost and changeover
cost renders the results presented in this section. The results are presented for the three
49
levels SKU, recipe-group and Line. The selection of SKUs for the results in this section is
guided by previously used SKUs in the analysis, complemented with other SKUs to capture
examples from various recipe-groups and all studied lines.
The calculated batch sizes for a selection of recipe groups are presented in Figure 15
together with the average batch sizes the last 12 months.
Figure 15. Average batch size per recipe-group.
In all of the presented recipe-groups, the average batch sizes increased compared to the
average batch size of the recipe-groups during the last 12 months. Representations of
recipe-groups from all studied lines are included In Figure 15. The analysis is performed for
when both βπΈππ and βπΉπ΅πΊ are used in the EOQ formula. As expected the batch size is larger
when βπΉπ΅πΊ is used, as βπΉπ΅πΊ < βπΈππ.
If the same analysis is performed on a SKU-level the results show that both increased and
decreased batch sizes exist. The analysis is presented in Table 8 below which include
articles from the same recipe-groups as figure 15.
Table 8. Average batch sizes for a selection of SKUs
50
The average batch size on the lines are presented in figure 16.
Figure 16 Average batch sizes on the four studied lines.
On a line-level the average batch size increase when the EOQ-formula is used, compared to
the size of the average batch during the last 12 months.
Finally, an analysis has been made for one product to support or reject the suggested fact
that deviating from the calculated batch size has a limited impact on the average costs.
Figure 17 shows the cost for a value Q, using (1), with the optimal Q Β± 20% being shown
between the dotted lines. It can easily be seen that within this interval the cost is a relatively
constant function of the batch size. As long as the Q is chosen in this interval, the cost does
not deviate much from its minimum.
51
Figure 17 cost analysis when deviating from optimum batch size
This finding is supported by the theory in that the total cost is not affected much when the
chosen Q deviate relatively little from the resulting Q from the EOQ model.
5.8 Safety Stock
This chapter will study the implications of the current safety stock formula and the
consequences changing the batch sizes will have on the safety stock. A new theoretically
sound method to calculate the safety stock is also proposed.
5.8.1 Implication of current setup
Recall from chapter 4 that the company currently uses a safety stock formula based on
delivering a certain cycle service level S1 (proportion of stock cycles without a stockout). At
the same time their operations are evaluated upon their stock service level, S2, defined in
chapter 4. This implicates a discrepancy in how the safety stock is calculated and how it is
later evaluated.
The implications of (16), shown again below, is that increasing the average batch size for an
SKU, with all other variables remaining fixed, will also increase the safety stock of this SKU.
This increase can be especially substantial if the supplier variability, (PE.CT), for the SKU is
high.
ππ = π β β(πΏπ β ππΉπΈ2 ) + (ππΈ. πΆπ) β π2 (16)
In a further analysis of the last six months, both S1 and S2 are calculated using observed
historical data. S1 is the fraction of weeks that had no stock out divided by the total number
0
10000
20000
30000
40000
50000
60000
Cost analysis of product X
Changeover Cost Holding Cost Total Cost
52
of weeks and S2 is the fraction of delivered volume divided by all ordered volume. The
resulting S1 is way off the target service level while the resulting S2 more closely follows the
requested one. Table 9 below shows the result from the six months in S1 and S2 for the 10
SKUs with the highest sales volume.
Table 9: Last six months service level for the 10 SKUs with highest sales volume, as observed, and the target βstock service levelβ.
The company is using a safety stock formula that does not properly reflect their way of
measuring their operations. The resulting S1 is not following the target while the resulting S2,
that is not currently part of the safety stock calculation, seem to follow the target more
closely. The simplest explanation for this is that the input data for the safety stock formula
are not correct, resulting in a lower resulting S1 for the used safety stock. The company
obtain better results in their fill rate even though it is not a part of their safety stock
calculation, something that might have several explanations.
1. The safety stock calculated using S1 might coincidentally be a good fit.
2. The operational planning team is manually changing the plan when unforeseen
events occur to ensure supply availability.
3. The safety stock does not make a significant impact on the service level due to
constant high stock levels.
Not much can be said about the first point more than that it is highly unlikely that the
companyβs homemade formula can make a good calculation for all SKUs. The second point
would indicate a lot of time spent on βfire-fighting by the operational team, working in a
reactionary way solving problems as they arise instead of staying proactive. Since a stock
out would cause a bigger immediate reaction from the organization than stock building it
would be natural to push a higher production than strictly needed. The third point indicates
that the stock is constantly higher than needed to keep the requested service level, most
likely due to stock building situations.
An important fact to remember is that the safety stock is designed to meet a requested
service level. The desired outcome is that the resulting service level equals the request and it
should be neither higher nor lower. Calculating the safety stock in an incorrect manner might
53
not only result in too low service level but also a too high, resulting in excessive costs. The
historical data of the last six months reveal that 113 of 176 (64,2%) articles have had a
higher fill rate than 99.3%, which is the highest target.
The data shows that SKUs with a high sales volume show results close to the requested S2
while showing a considerably lower S1 than requested, while many low-volume SKUs
sustain a higher fill rate than necessary. This strongly implicate that the resulting S1 does not
reflect the calculations that have been made for safety stock and in turn that the current
safety stock calculation is essentially inconsequential to the resulting service level, most
likely due to operational manual adjustments.
With this in mind, the second and third point seem both seem to be reasonable. Keeping a
high stock due to stock building in production helps keep the service level up even with a
poor safety stock calculation. When outside of a stock building phase the second point seem
like a good explanation for the high-volume articles, the ones that make the biggest impact
on warehousing operations, stay close to the target service level while smaller articles keep a
too high service level in general.
5.8.2 A new suggestion
To summarise the last chapter, the company is evaluated on their fill rate, S2, while
dimensioning their safety stock in accordance to a formula originating from a S1 approach.
The implications of using the formula for fill rate presented in chapter 2 is evaluated in this
section.
Reminding the reader of the formula to determine safety stock that corresponds with a
service level S2 under Normally distributed customer demand.
π2 = 1 βπβ²
πβ [πΊ (
ππ
πβ²) β πΊ (
ππ + π
πβ²)] (8)
Noting that the loss function (G(x)) is strictly decreasing with an increasing input it can be
concluded that an increased Q contribute to lower the safety stock in this formula.
A weakness with this formula is that it does not consider the supply reliability, and since the
companyβs production lines suffer from a high degree of variation in yield of the batches this
can result in a non-reliable safety stock.
So, is there any way to amend the standard deviation term of the formula to include the yield
variation of the production lines? Johan Marklund, professor at Lund University and the
thesis supervisor suggested to include the yield loss as an increase in customer demand
during the period. This would mean that a loss in yield is modelled as an increase in demand
and thus contributing to a higher variation.
From chapter three it is known that two independent stochastic variables that are normally
distributed can be summed by combining them as
54
π + π β π (ππ + ππ, βππ2 + ππ
2)
In chapter three it is also suggested that yield can be modeled using a stochastic variable,
the quotient of the planned volume that is completed as output. In the literature it is
suggested that πππππ β [0,1] but since the yield can be over 100% in this case, this is
extended to πππππ β [0, β]. The same reasoning applies to the yield loss, which simply
equals 1 β yield. The conclusion is that the yield loss is also a stochastic variable,
ππππππππ π β [ββ, 1].
This stochastic variable belongs to an arbitrary distribution, but if this distribution can be
approximated as normal a solution to the problem have been found.
The deviation of the forecast has already been shown, in section 5.4, to be normally
distributed. It is fair to assume that the customer demand and the yield loss of the production
lines are independent. The yield loss has no connection to the forecast accuracy, and vice
versa.
The only thing remaining is then to show that it is reasonable to assume that the yield loss is
normally distributed. To find the yield loss, the measurement production fulfillment is used,
which equals the measure yield in the literature. The yield-loss is simple to derive from the
production fulfillment data in the same way it is from yield.
πππππ πΏππ π = 1 β πππππ’ππ‘πππππ’πππππππππ‘
Data from the last year was pulled from the system and a histogram were made of the
production fulfillment for 52 weeks. This is presented in Figure 18.
Figure 18: Histogram of yield loss in percent for Line Y, a negative yield loss means the produced quantity was larger than the planned.
The data suggest that while far from perfect, the normal distribution is at least fair to use with
regards to the production fulfillment. Since this is the only distribution that would work well
with the chosen approach, the hypothesis that πππππ’ππ‘πππ πΉπ’πππππππππ‘ β π(π, π2) is
55
accepted without further investigation. Table 10 below shows the calculated mean and
standard deviation of the yield loss for the four studied lines.
Table 10: Mean and standard deviation of yield losses for the lines in this study, note that it is displayed in units of percent.
To make sense of this combination, the yield loss from production can be interpreted as an
increase in demand, as the volume lost in production might just as well have been a
customer coming in to make a last-minute order of more volume. The combined stochastic
variables of customer demand and production yield loss therefore create the new variable
that we simply call demand.
The resulting standard deviation used in the formula is, consequently:
πβ² = βππ·β² 2
+ ππβ² 2
ππ·β² = π π‘ππππππ πππ£πππ‘πππ ππ ππ’π π‘ππππ ππππππ ππ π»πΏ(π»πππ‘ππππ‘πππ ) ππ’ππππ πππππ‘πππ
ππβ² = π π‘ππππππ πππ£πππ‘πππ πππ π¦πππππππ π ππ πππππππ‘ π‘ππππ π‘βπ πππ‘πβπ ππ§π ππ π»πΏ ππ’ππππ πππππ‘πππ
The result of the new equation is that the batch size βpullsβ in two different directions. To
increase the safety stock due to the yield loss aspect and to decrease safety stock due to a
higher fraction on time with higher stock. This is a more correct representation than the
current method used and will not result in a flat increase of all articles on safety stock if batch
sizes are increased but rather only if the yield variation demands it.
The resulting formula for safety stock is, consequently, (8), where the standard deviation
used is the one obtained as:
πβ² = βππ·β² 2
+ ππβ² 2
π2 = 1 βπβ²
πβ [πΊ (
ππ
πβ²) β πΊ (
ππ + π
πβ²)] (8)
While hard to solve algebraically, one can easily solve for the safety stock numerically using
a computer.
56
5.9 Effects on finished goods inventory
The new way of calculating safety stock, combined with the new batch sizes calculated with
the EOQ model results in a dramatical decrease by about 35% in the total safety stock for
the studied SKUs.
This result is a consequence of not only penalizing the safety stock when the batch size
increases for an SKU, but also include a parameter that considers the increased fraction of
time spent with no real risk for stock out. A high variability in yield of the line producing the
SKU leads to an increase in safety stock when the batch size increases. On the other hand,
the increased batch size reduces the need for safety stock due more time spent with no real
risk of stockout. Figure 19 below shows the change in safety stock.
Figure 19: Safety stock for new suggestion and Current setup
Figure 19 visualize the reduction of safety stock for the new suggestion compared to the
current setup. A reduction could be found both when βπΈππ and βπΉπ΅πΊ are used.
The average new stock on hand is calculated as:
π΄π£πππππ π π‘πππ ππ βπππ = ππ +π
2
Figure 20 present the aggregated average stock on hand, of the SKUs produced at the lines.
57
Figure 20 Contributions of average stock on hand from the studied lines.
The new suggestion to calculate the safety stock reduce the safety stock compared to the
current setup. The batch sizes from the EOQ-model increase the average batch size and
therefore contributes to a larger stock on hand. Figure 20 indicate that in todayβs operations
with pallets stored at external warehouses, these changes which influence the average stock
on hand in different ways, together has little effect compared to the current setup.
5.10 Effects on production
With the calculated batch size from the EOQ formula, further analysis can be made.
Derivation of parameters such as average coverage time for a batch, which is the time a
batch will stay in stock until depleted could be calculated as:
π΄π£πππππ πππ£πππππ π‘πππ =π
π(22)
The coverage time is what will be used to guide the cycle planning of the articles i.e. between
what time interval specific articles should be produced.
The average production hours per week required to satisfy demand is calculated by
multiplying the weekly demand with the time used to produce one piece of the SKU which is
based on the expected production rate.
πππππ’ππ‘πππβππ’ππ πππ π€πππ = π· β1
πΈπ₯ππππ‘ππ πππππ’ππ‘πππ πππ‘π (23)
πΈπ₯ππππ‘ππ πππππ’ππ‘πππ πππ‘π = πππ₯πππ’π πππππ’ππ‘πππ πππ‘π β ππ₯ππππ‘ππ ππΈπΈ.
The expected production rate is based on how efficient the line is operating i.e. it is the
nominal production rate scaled down with the OEE. This metric is not changed by the EOQ
but static with the demand and production rate.
58
The average changeover time which is calculated per week, is calculated by inverting the
average coverage time which gives the average number of changeovers per week.
π΄π£πππππ πβππππππ£ππ π‘πππ πππ π€πππ = π΄π£πππππ πππ£πππππ π‘πππβ1 β πβππππππ£ππ π‘πππ (24)
This metric is highly dependent on the EOQ. By combining the average time to produce for
each week with the average time for changeover, for each article on a line one can see how
much time needs to be allocated to the line each week, and if the current capacity is enough
to handle it. Table 11 present the calculated parameters for the selection of SKUs, previously
used.
Table 11. Calculated parameters for the selection of articles
The producing time and changeover time can be combined to obtain the average required
production time per week for each SKU. The production time is the average required time per
line and week, to meet the average demand. From a planning perspective the required
production times of the SKUs are of great interest. Table 12 present the results of the
needed capacity for the analyzed lines.
Table 12. Production time per week
The table indicate that Line I does not have enough capacity. Lack of capacity needs to be
addressed with sourcing. A possible way for improvement would be to increase the number
of shifts. This is not an option on Line I since it already has 5 shifts. One should bear in mind
that this analysis includes all articles scaled down to a week. Due to seasonality, for some
SKUs the need for production seldom occurs throughout the year. One should also bear in
mind that an increase of shifts has effects on other parts of the supply chain such as
processing and the warehouse.
Table 12 show that the production time is higher with (βπΈππ) than (βπΉπ΅πΊ). The production time
includes both the changeover time and the production time to cover the demand during the
59
coverage time. The times are normalised to a week. Figure 21 show how these times relate
to each other when the different holding costs are applied.
Figure 21: Changes is production time and changeover times at the lines.
The figure illustrates that the production time per week to cover the demand during the
coverage time are the same. What is reducing the production time is the changeover time.
This analysis illustrate that larger batch sizes increases the theoretical OEE which enables
more efficient usage of the resources and less open time for the same volume.
From the insights of the required time in Table 12, possible discrepancies can be acted upon.
If the needed capacity exceeds the open time several strategic options are available such as
invest in production capacity by increasing the number of shift or invest in equipment. Such
analysis is out of scope for the model.
Two tactical decisions can be identified related to the issue with limited capacity. The
company is currently handling it in two ways, increase the stock or outsource some of the
volume.
5.11 Cycle planning
This section presents how the cycle planning is taken into consideration. The procedure uses
the coverage time presented in the previous section. A summary of each recipe group is
made to guide the user to a fitting cycle for the recipe group. In the example in Table 13,
eight SKUs belonging to the same recipe is showed with the coverage time of the batch size
resulted from the previous steps. This coverage time is then altered for all the SKUs to make
them share a common denominator and thus able to share cycle. Note that this table will
suggest batch sizes not calculated through the minimum cost approach, which should be
understood by users in their operational work.
60
Table 13: The Cycle-planning helper.
5.12 Summary
With the objective to create a quantitative model to determine production batch sizes and
evaluate the consequences on the warehouse and production operations, several key areas
have been analysed.
A mathematical model was first chosen to find the batch sizes that entail the lowest cost to
the supply chain, the EOQ-model. This model was chosen based on a pro-con approach,
comparing it to other models, with the companyβs supply chain characteristics kept in mind.
Input values were then produced to be used as input data in the model, and three equations
were presented to calculate these were produced. This resulted in (18), (19) and (20).
ππΆπΆππΎπ = πΆπ + (πΆβ β π‘π) (18)
βπΈππ = (β π π
ππ=1
ππΈππ+ ππΆπ) β
1
πππΎπ
(19)
βπΉπ΅πΊ = (β π π β ππ
ππ=1
ππΉπ΅πΊ+ ππΆπ) β
1
πππΎπ
(20)
The resulting batch sizes of the model were presented and compared to the current average
batch sizes. The determined batch sizes, as calculated in the model, are generally larger
than the historical average. Aggregated on a line level, the new average is higher for all lines.
It is also shown that if the main warehouse would be expanded, the resulting batch sizes
would be greater still.
With the new economic order quantities in hand, an approach to solving the perishability
problem was analysed. By using a statistical analysis of historical forecast accuracy, and the
future demand, a maximum batch size was introduced. This maximum batch size is
determined to allow no more than a 5% risk that goods will perish, and it may reduce the
EOQ-quantity.
61
Early in the project the companyβs current safety stock formula was identified to be
contingent on the chosen batch sizes, and an effort to gauge the consequences to the safety
stocks when altering the batch sizes were made. This analysis identified problems with how
the company currently calculates their safety stocks. An evaluation of the current approach
was made and an alternative suggestion to solve the problems was then introduced. The
new solution greatly decreases the total safety stock level, reducing many SKUs safety stock
while increasing it for a smaller number of SKUs.
We concluded the chapter by illustrating the impact using our model can have on the finished
goods and production departments, showing a slight increase in total stock and a decrease
in changeover time for the production when using the new batch sizes and safety stock
calculations.
62
63
6 Model Outline
In this chapter, we present the Excel-model that is handed over to the company. The
objective of the chapter is to give the reader an understanding of the work done with the
model and how it uses the analytical conclusions to create value to the companyβs
operations.
The model first uses the input values for each SKU to calculate an economic order quantity.
This quantity is then compared to the maximum batch size and the feasible batch sizes for
the SKU and is modified accordingly. The resulting batch size is then used both to provide
management with an idea of how much capacity is needed for the line, and to help the
operational planners in their work.
6.1 Application of the Model
A suggestion is to apply the model and determine new batch quantities in connection to the
updates of the safety stock levels, which currently take place once every six months. This is
a suitable time to change the batch sizes since the batch sizes is an input to the safety stock
formula the company is using. In this way, the model will serve as a tool on a tactical level.
We suggest that these tactical batch sizes are extended to the operative planning process by
letting them constitute the fixed choice in SAP and serve as a guidance for the planners.
6.2 Model procedure
The core is the EOQ model, while the rest is suggested to consist of βtiersβ that will be used
to modify the EOQ solution according to operational planning constraints and characteristics.
Figure 22 shows the idea in a graphical way to visualize what the tiers will consist of and how
they work. First the EOQ model will produce a preliminary batch size according to the
strengths and weaknesses of the model (See 5.1). After this, the succeeding tiers will alter,
or suggest an alteration, for the batch size to fit with operational parameters. The effects on
the finished goods inventory and production are thereafter analysed. Lastly, the cycle
planning for the SKUs in the recipe groups are determined.
Figure 22: Tiers of suggested model
64
The flowchart in Figure 23 below describes the procedure for determining the batch sizes. The first step of the model is the EOQ calculation, executed with the values obtained in chapter 5. The resulting batch sizes are then compared to the maximum batch quantity for the considered SKU, derived in chapter 5, and scaled down if needed. Continuing, the batch size is altered in accordance with the operation constraints of the process, presented in chapter 4.
Figure 23: Flowchart of working model procedure.
The model will determine the final quantity based on constraints for the minimum batch size
and the calculated maximum batch size, choosing the closest feasible Q to Q* within the
accepted interval. This is illustrated in Figure 24 where the bars illustrate the feasible batch
sizes. The minimum and maximum batch sizes determine the interval of feasible batch sizes.
65
Figure 24. Illustration of selection of possible batch sizes.
6.3 Model procedure to evaluate effects.
The determined batch sizes and the calculated parameters are used to evaluate the effects
on the production operations and the finished goods inventory. The batch sizes and the
calculated parameters are in the model structured in a table, see Table 14. Pivot tables are
applied on the data in the table to aggregate the production time, safety stock and average
stock for the SKUs, on each line.
Table 14. Data aggregated to evaluate effects on production and finished goods inventory for a selection of SKUs across the 4 lines included in the report.
Reminding the reader that the fourth column, coverage time, is used to determine cycle time
as previously explained.
6.4 Input Data
The format of the input data for the model, and what data is needed, is of vital importance for
the usage of the tool. The need for simplicity is strong and it is preferable that all data used in
the model to be readily available in report formats.
The tool requires several kinds of input data. This data is divided in five different categories,
shown in Figure 25.
66
Figure 25: The different input categories of the model
The companyβs Business Intelligence tool have been found to be the best tool to handle this,
as reports can be crafted to essentially match any need. Most of the data needed can be
taken directly from the system but some of it must be modified slightly to fit the required
format of the model. An example of this is the average changeover time per recipe group
where the report returns historical productions orders and the user needs to create an
average per recipe group.
Each input category is a separate sheet in the model except for the historical forecast error.
The data over the historical forecast error are used in another sheet where the maximum
batch sizes are calculated.
67
7 Discussion
The purpose of this project was to derive a quantitative model which determines the batch
sizes in a better way and evaluate the impact of potential changes in the supply chain. The
project was initiated by the planning department to bring consensus between various entities
in the supply chain by using facts and figures. One obvious problem which complicates the
development of the model is the complex supply chain with a vast number of articles and
limited capacity, which most of the available theoretical models do not include. This
complication is especially experienced at the planning department which must plan for
different ambitions from various departments in the company. The literature has pointed out
this problem and highlighted it as a strategic problem and thus the created model is
suggested to be a tactical tool to guide the activities in the operational planning.
Consequently, the model is not created to solve the complex problems of the supply chain
but rather to focus on providing a cost-based solution for the supply chain which can be used
as a baseline for operative work.
On a tactical level, the company uses S&OP as a business processes to handle the complex
supply situation. The effort put in to handle the supply situation on a tactical level indicates
that strategic decisions as investments in assets, facilities or product portfolios might need to
be reviewed to operate in a better way. Such analysis is outside of the scope of this project
but pointed out as potential for improvement of the performance of the supply chain.
7.1 Sensitivity analysis
The current analysis is made using data from last yearβs operations. As the production and
warehouse operations are subject to constant change (and hopefully improvement). The
statistical parameters of the stochastic variables derived in the analysis are also subject to
change. This primarily affect the costs used for the EOQ-model as well as the forecast-
accuracy of the demand, and these should be revised as time goes on. For the maximum
batch sizes, relatively small changes in the standard deviation of the forecast accuracy can
have a large impact on the maximum batch sizes and expected volume of perished goods.
Changes in the standard deviation of yield from the lines and the demand accuracy also
have significant impact on the safety stock calculations and a reduction of these can lead to
reductions in the total stock. One should be aware of the assumptions regarding for
independent stochastic variables, used in the linear combinations. If strong correlations are
present, the safety stock calculations and the modifications of the EOQ solution are affected.
Assumptions have been made for βπΉπ΅πΊ, which affect the results from the EOQ-Model.
However, as discussed in section 5.7, the EOQ-model is relatively robust to errors in the
input parameter.
Finally, the EOQ-formula works best when the demand is relatively stable. SKUs that show a
big variation in demand should have the timeframe of the collected critical values lowered,
thus increasing the frequency of the analysis, for it to be accurate.
68
7.2 Scientific contribution
The purpose of the report was mainly to solve a problem provided by the company and most
of the effort have been given to this task. However, the thesis can be used as a reference of
how to handle various decisions in an industry with similar characteristics to the one
examined. These include a complex portfolio and relatively clear warehousing costs.
This project contributes with a new approach where the results from the EOQ-formula is
adjusted based on perishability and constraints in the manufacturing. In addition, the way of
modeling the holding cost vary from the most common way used in industry by using an
activity-based costing approach instead of the same holding cost rate for every SKU.
The way of modeling the safety stock including the yield loss in the fill rate formula is found
not to be not commonly used in theory. This report used these relatively new approaches in a
case study with relevant results.
7.3 Areas for future improvement
As with most research, there are always room for further investigation. Related to the holding
cost for the extended main warehouse, assumptions for the marginal fraction have been
made. These assumptions are suggested to be reviewed by people with expert knowledge of
the warehouse operations.
Another area to further investigate is the changeover costs and the suggestion of including
fixed overhead costs such as depreciation to the changeover cost for lines with capacity
limitations. This was rejected, since no theory was found to support this.
The batch sizes determined by the model are suggestions on a tactical level for the
upcoming six months. It is likely that the suggestions from the model will be changed in the
operative planning process due to complexity reasons. To handle the alterations of the batch
sizes in the operative planning process, an extension of the model, or perhaps separate
complementing model are identified as opportunities to guide the operative planning process.
Trade-off analysis could be performed to point out the best alterations for the situation.
For some SKUs, best practice would be to decrease the timeframe of the calculation
because of a variating demand due to seasonal effects. A suggested development of the
model is therefore to build in more detailed way to model the demand during specific time-
periods based on characteristics for the articleβs demand. This would result in a higher
frequency of changing the batch size that would better reflect the changes in demand during
the year. The negative part of this is, naturally, the increased complexity and the increased
workload of using the model more frequently.
69
8 Summary and Conclusions
The current method of determining the batch sizes at the company relies heavily on the
individual plannerβs experience and empirical knowledge. The planning management wanted
to investigate how the quantities of the production orders can be better chosen based on
costs in the supply chain. They therefore requested a quantitative model which could guide
the planning department in their future work. Therefore, the projectβs purpose was set to
create a quantitative model that takes relevant costs and variables into account when
determining the production batch sizes. The objective was also to evaluate the impact the
model would have on finished goods inventory and the production capacity.
The companyβs current supply chain structure has been examined and the costs in this
supply chain that relate to the batch sizes have been modeled in a straightforward manner.
The approach to modeling the holding cost stock have been conducted with an activity-based
costing approach. A solution for cost modeling of the sourcing aspect in the changeover cost
have also been presented.
The model alters the batch size from the EOQ-formula when the risk of perished goods and
the constraints of the processing department are considered. The model can be used for
investigating the production and warehousing operations. For example, an analysis of how
the new warehouse project would affect the stock and production capacity is presented.
To conclude, relevant theoretical models to determine batch sizes exist. The best choice of
model for the company has been concluded to be the EOQ-Model, because of its simplicity
and robustness. When this theory is incorporated in our model together with analysis of
perished goods and constraints in processing, the model indicates that larger batch sizes
than today should be used. An extension of the warehouse is assumed to decrease the
holding cost and therefore increase the batch sizes further.
Regarding the consequences on the supply chain, the analysis of required production
resources indicate that the limited capacity would require sourcing of products, even with the
changed batch sizes.
A special finding concerns the companyβs current safety stock formula. The company is
currently dimensioning their safety stock levels based on a formula that calculates the
probability of no stock out per order cycle, but they are evaluated on the fill rate. With
continuous usage of the current formula, the safety stock, and thus the average inventory
would increase with increased batch sizes. A proposed suggestion of how to calculate the
safety stock which incorporate the yield loss, is developed in collaboration with Johan
Marklund, the supervisor of this project at Lund University. The new suggestion together with
the increased batch sizes, result in a reduced safety stock. These changes result in a
minimal change to the average stock on hand. The most effective way to further decrease
the safety stock for the company is to lower the variability of the production yield.
70
71
9 Recommendations
The recommendation to the company is to start using the provided model to determine the
batch sizes.
To make sure the model works accurately, the input data must be maintained and updated.
The planning department is suggested to review the parameters every time the model is
used, for example by inviting representatives from the different departments to evaluate the
costs used. The company is suggested to put more effort into determine a holding cost for
the extended warehouse.
This report brings attention to the companyβs safety stock formula, derived from a stock out
probability per order cycle perspective and not ready rate which the supply chain is
measured on. A new suggestion of how to calculate the safety stock based on the fill rate
which incorporated the yield loss, is suggested.
Opportunities to further develop the model have also been identified. Firstly, the user
friendliness which is especially apparent in the process of updating parameters such as cost
or article data. Two other opportunities relate to possible extensions of the model. The first
one is to incorporate seasonality, and the second is to better visualise consequences of
changing the batch size from the initial suggestion.
72
73
10 References
AxΓ€ter, S., 2006. Inventory Control. 2nd ed. Lund: Springer Science.
Berling, P., 2005. On Determination of Inventory Cost, Lund: Department of Industrial
Management and Logistics .
Blom, G. et al., 2005. Sannolikhetsteori och statistikteori med tillΓ€mpningar. 5th ed. Lund:
Studentlitteratur.
Bryman, A. & Bell, E., 2011. Business Research Methods. 3rd ed. Cambridge; New York:
Oxford University Press.
Cohen, L., Manion, L. & Morrison, K., 2000. Research Methods in Education. 5th ed. New
York: RoutledgeFalmer.
Freytag, P. V. & Young, L., 2018. Collaborative Research Design. 1st ed. Singapore:
Springer Nature.
Grimson, A. J. & Pyke, D. F., 2007. Sales and operations planning: an exploratory study and
framework. The International Journal of Logistics, 18(3), pp. 322-346.
Harris, W. F., 1913. How many parts to make at once. Factory, The magazine of
management, Volume 10, pp. 135-136, 152.
Hill, A. & Hill, T., 2009. Manufacturing Operations Strategy. 3rd ed. Houndmills: Palgrave
Macmillan.
Hopp, W. J. & Spearman, M. L., 2001. Factory Physics: Foundations of Manufacturing
Management. 2nd ed. New York: The McGraw-Hill Companies, Inc.
Hosang, J., Frank, C. F. & Jeong, B., 2007. Trends in Supply Chain Demand and
Management. London: Springer.
HΓΆst, M., Regnell, B. & Runeson, P., 2006. Att genomfΓΆra ett examensarbete. 1:6 ed. Lund:
Studentliteratur AB.
Johnson, G., Whittington, R., Scholes, K. & Angwin, D., 2015. Fundamentals of Strategy. 3rd
ed. Edinburgh : Pearson Education Limited.
King, P. L., 2011. Crack the Code - Understanding safety stock and mastering its equations.
APICS-magizine, pp. 33-36.
Kotzab, H. & Westhaus, M., 2005. Research methodologies in supply chain management.
(eds) ed. New York: Physica-Verlag HD.
Laguna, M. & Marklund, J., 2013. Business Process Modeling, Simulation and Design. 2nd
ed. s.l.:CRC press.
Nelson, M., 2005. The Barbarian's Beverage: A History of Beer in Anciant Europe. 1st ed.
New York: Routledge.
Runesson, P. & HΓΆst, M., 2009. Guidelines for conducting and reporting case studyresearch
in software engineering. Empir Software Eng, Volume 14, pp. 131-164.
Silver, E. A. & Meal, H. C., 1973. A Heuristic for Selecting Lot Size Requirements for the
Case of Deterministic Time-Varying Demand Rate and Discrete Opportunities for
Replenishment. Production and Inventory Management, Issue 14, pp. 64-74.
SkΓ€rvad, P.-H. & Olsson, J., 2005. FΓΆretagsekonomi 100. 11 ed. MalmΓΆ: Liber Ekonomi.
Sonntag, D. R., 2017. Safety stock determination in production systems with random yield
and positive lead times, Magdeburg: Otto von Guericke University.
Wallace, T. F. & Stahl, A. R., 2008. Sales and Operations Planning The How-To Handbook.
3rd ed. Montgomery: T. F. Wallace & Company.
Wikner, J. & Noroozi, S., 2017. Sales and operations planning in the process industry: A
literature review. International Journal of Production Economics, 188(7), pp. 139-155.
74
Yin, R. K., 2014. Case Study Research: Design and Methods, Los Angeles: Sage
publications.